Understanding Exponents - Math

Card 0 of 20

Question

Simplify the expression:

$\small (16^{\frac{1}{2}})(256^{\frac{3}{4}})$

Answer

Remember that fraction exponents are the same as radicals.

$\small 16^{\frac{1}{2}}=\sqrt{16}=4$

$256^{\frac{3}{4}}=\sqrt[4]{256^3}=64$

A shortcut would be to express the terms as exponents and look for opportunities to cancel.

$16^{\frac{1}{2}}=(4^2)^{\frac{1}{2}}=4$

$\small 256^{\frac{3}{4}}=(4^4)^{\frac{3}{4}}=4^3=64$

Either method, we then need to multiply to two terms.

$\small (4)(64)=256$

Compare your answer with the correct one above

Question

Convert the exponent to radical notation.

$x^{\frac{3}{7}}$

Answer

Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

$x^{\frac{3}{7}}=\sqrt[7]{x^3}$

Compare your answer with the correct one above

Question

Which of the following is equivalent to $64^{\frac{1}{2}}$ ?

Answer

By definition, a number raised to the $\frac{1}{2}$ power is the same as the square root of that number.

Since the square root of 64 is 8, 8 is our solution.

Compare your answer with the correct one above

Question

Solve for :

$(x+5)^{-3} = -1$

Answer

Raise both sides of the equation to the inverse power of to cancel the exponent on the left hand side of the equation.

$\rightarrow ((x+5)^{-3})^{-\frac{1}{3}} = (-1)^{-\frac{1}{3}}$

$\rightarrow x+5 = -1$

Subtract from both sides:

$\rightarrow (x+5) - 5 = (-1)-5$

$\rightarrow x = -6$

Compare your answer with the correct one above

Question

Which of the following is equivalent to $3^{-2}$ ?

Answer

By definition,

$b^{-x} = \frac{1}{b^{x}}$ .

In our problem, and .

Then, we have $\frac{1}{3^{2}} = \frac{1}{9}$ .

Compare your answer with the correct one above

Question

Simplify the expression:

$\small (16^{\frac{1}{2}})(256^{\frac{3}{4}})$

Answer

Remember that fraction exponents are the same as radicals.

$\small 16^{\frac{1}{2}}=\sqrt{16}=4$

$256^{\frac{3}{4}}=\sqrt[4]{256^3}=64$

A shortcut would be to express the terms as exponents and look for opportunities to cancel.

$16^{\frac{1}{2}}=(4^2)^{\frac{1}{2}}=4$

$\small 256^{\frac{3}{4}}=(4^4)^{\frac{3}{4}}=4^3=64$

Either method, we then need to multiply to two terms.

$\small (4)(64)=256$

Compare your answer with the correct one above

Question

Convert the exponent to radical notation.

$x^{\frac{3}{7}}$

Answer

Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

$x^{\frac{3}{7}}=\sqrt[7]{x^3}$

Compare your answer with the correct one above

Question

Which of the following is equivalent to $64^{\frac{1}{2}}$ ?

Answer

By definition, a number raised to the $\frac{1}{2}$ power is the same as the square root of that number.

Since the square root of 64 is 8, 8 is our solution.

Compare your answer with the correct one above

Question

Solve for :

$(x+5)^{-3} = -1$

Answer

Raise both sides of the equation to the inverse power of to cancel the exponent on the left hand side of the equation.

$\rightarrow ((x+5)^{-3})^{-\frac{1}{3}} = (-1)^{-\frac{1}{3}}$

$\rightarrow x+5 = -1$

Subtract from both sides:

$\rightarrow (x+5) - 5 = (-1)-5$

$\rightarrow x = -6$

Compare your answer with the correct one above

Question

Which of the following is equivalent to $3^{-2}$ ?

Answer

By definition,

$b^{-x} = \frac{1}{b^{x}}$ .

In our problem, and .

Then, we have $\frac{1}{3^{2}} = \frac{1}{9}$ .

Compare your answer with the correct one above

Question

Simplify the expression:

$\small (16^{\frac{1}{2}})(256^{\frac{3}{4}})$

Answer

Remember that fraction exponents are the same as radicals.

$\small 16^{\frac{1}{2}}=\sqrt{16}=4$

$256^{\frac{3}{4}}=\sqrt[4]{256^3}=64$

A shortcut would be to express the terms as exponents and look for opportunities to cancel.

$16^{\frac{1}{2}}=(4^2)^{\frac{1}{2}}=4$

$\small 256^{\frac{3}{4}}=(4^4)^{\frac{3}{4}}=4^3=64$

Either method, we then need to multiply to two terms.

$\small (4)(64)=256$

Compare your answer with the correct one above

Question

Convert the exponent to radical notation.

$x^{\frac{3}{7}}$

Answer

Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

$x^{\frac{3}{7}}=\sqrt[7]{x^3}$

Compare your answer with the correct one above

Question

Which of the following is equivalent to $64^{\frac{1}{2}}$ ?

Answer

By definition, a number raised to the $\frac{1}{2}$ power is the same as the square root of that number.

Since the square root of 64 is 8, 8 is our solution.

Compare your answer with the correct one above

Question

Solve for :

$(x+5)^{-3} = -1$

Answer

Raise both sides of the equation to the inverse power of to cancel the exponent on the left hand side of the equation.

$\rightarrow ((x+5)^{-3})^{-\frac{1}{3}} = (-1)^{-\frac{1}{3}}$

$\rightarrow x+5 = -1$

Subtract from both sides:

$\rightarrow (x+5) - 5 = (-1)-5$

$\rightarrow x = -6$

Compare your answer with the correct one above

Question

Which of the following is equivalent to $3^{-2}$ ?

Answer

By definition,

$b^{-x} = \frac{1}{b^{x}}$ .

In our problem, and .

Then, we have $\frac{1}{3^{2}} = \frac{1}{9}$ .

Compare your answer with the correct one above

Question

Simplify the expression:

$\small (16^{\frac{1}{2}})(256^{\frac{3}{4}})$

Answer

Remember that fraction exponents are the same as radicals.

$\small 16^{\frac{1}{2}}=\sqrt{16}=4$

$256^{\frac{3}{4}}=\sqrt[4]{256^3}=64$

A shortcut would be to express the terms as exponents and look for opportunities to cancel.

$16^{\frac{1}{2}}=(4^2)^{\frac{1}{2}}=4$

$\small 256^{\frac{3}{4}}=(4^4)^{\frac{3}{4}}=4^3=64$

Either method, we then need to multiply to two terms.

$\small (4)(64)=256$

Compare your answer with the correct one above

Question

Convert the exponent to radical notation.

$x^{\frac{3}{7}}$

Answer

Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

$x^{\frac{3}{7}}=\sqrt[7]{x^3}$

Compare your answer with the correct one above

Question

Which of the following is equivalent to $64^{\frac{1}{2}}$ ?

Answer

By definition, a number raised to the $\frac{1}{2}$ power is the same as the square root of that number.

Since the square root of 64 is 8, 8 is our solution.

Compare your answer with the correct one above

Question

Solve for :

$(x+5)^{-3} = -1$

Answer

Raise both sides of the equation to the inverse power of to cancel the exponent on the left hand side of the equation.

$\rightarrow ((x+5)^{-3})^{-\frac{1}{3}} = (-1)^{-\frac{1}{3}}$

$\rightarrow x+5 = -1$

Subtract from both sides:

$\rightarrow (x+5) - 5 = (-1)-5$

$\rightarrow x = -6$

Compare your answer with the correct one above

Question

Which of the following is equivalent to $3^{-2}$ ?

Answer

By definition,

$b^{-x} = \frac{1}{b^{x}}$ .

In our problem, and .

Then, we have $\frac{1}{3^{2}} = \frac{1}{9}$ .

Compare your answer with the correct one above

Tap the card to reveal the answer

Understanding Exponents - Math

Simplify the expression:

Remember that fraction exponents are the same as radicals. A shortcut would be to express the terms as exponents and look for opportunities to cancel. Either method, we then need to multiply to two terms.

Convert the exponent to radical notation.

Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.

Which of the following is equivalent to ?

By definition, a number raised to the power is the same as the square root of that number. Since the square root of 64 is 8, 8 is our solution.

Solve for :

Raise both sides of the equation to the inverse power of to cancel the exponent on the left hand side of the equation. Subtract from both sides:

Which of the following is equivalent to ?

By definition, . In our problem, and . Then, we have .

Simplify the expression:

Remember that fraction exponents are the same as radicals. A shortcut would be to express the terms as exponents and look for opportunities to cancel. Either method, we then need to multiply to two terms.

Convert the exponent to radical notation.

Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.

Which of the following is equivalent to ?

By definition, a number raised to the power is the same as the square root of that number. Since the square root of 64 is 8, 8 is our solution.

Solve for :

Raise both sides of the equation to the inverse power of to cancel the exponent on the left hand side of the equation. Subtract from both sides:

Which of the following is equivalent to ?

By definition, . In our problem, and . Then, we have .

Simplify the expression:

Remember that fraction exponents are the same as radicals. A shortcut would be to express the terms as exponents and look for opportunities to cancel. Either method, we then need to multiply to two terms.

Convert the exponent to radical notation.

Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.

Which of the following is equivalent to ?

By definition, a number raised to the power is the same as the square root of that number. Since the square root of 64 is 8, 8 is our solution.

Solve for :

Raise both sides of the equation to the inverse power of to cancel the exponent on the left hand side of the equation. Subtract from both sides:

Which of the following is equivalent to ?

By definition, . In our problem, and . Then, we have .

Simplify the expression:

Remember that fraction exponents are the same as radicals. A shortcut would be to express the terms as exponents and look for opportunities to cancel. Either method, we then need to multiply to two terms.

Convert the exponent to radical notation.

Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.

Which of the following is equivalent to ?

By definition, a number raised to the power is the same as the square root of that number. Since the square root of 64 is 8, 8 is our solution.

Solve for :

Raise both sides of the equation to the inverse power of to cancel the exponent on the left hand side of the equation. Subtract from both sides:

Which of the following is equivalent to ?

By definition, . In our problem, and . Then, we have .

Simplify the expression:

$\small (16^{\frac{1}{2}})(256^{\frac{3}{4}})$

Convert the exponent to radical notation.

$x^{\frac{3}{7}}$

Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

$x^{\frac{3}{7}}=\sqrt[7]{x^3}$

Which of the following is equivalent to $64^{\frac{1}{2}}$ ?

By definition, a number raised to the $\frac{1}{2}$ power is the same as the square root of that number.

Since the square root of 64 is 8, 8 is our solution.

Solve for :

$(x+5)^{-3} = -1$

Raise both sides of the equation to the inverse power of to cancel the exponent on the left hand side of the equation.

$\rightarrow ((x+5)^{-3})^{-\frac{1}{3}} = (-1)^{-\frac{1}{3}}$

$\rightarrow x+5 = -1$

Subtract from both sides:

$\rightarrow (x+5) - 5 = (-1)-5$

$\rightarrow x = -6$

Which of the following is equivalent to $3^{-2}$ ?

By definition,

$b^{-x} = \frac{1}{b^{x}}$ .

In our problem, and .

Then, we have $\frac{1}{3^{2}} = \frac{1}{9}$ .

Simplify the expression:

$\small (16^{\frac{1}{2}})(256^{\frac{3}{4}})$

Convert the exponent to radical notation.

$x^{\frac{3}{7}}$

Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

$x^{\frac{3}{7}}=\sqrt[7]{x^3}$

Which of the following is equivalent to $64^{\frac{1}{2}}$ ?

By definition, a number raised to the $\frac{1}{2}$ power is the same as the square root of that number.

Since the square root of 64 is 8, 8 is our solution.

Solve for :

$(x+5)^{-3} = -1$

Raise both sides of the equation to the inverse power of to cancel the exponent on the left hand side of the equation.

$\rightarrow ((x+5)^{-3})^{-\frac{1}{3}} = (-1)^{-\frac{1}{3}}$

$\rightarrow x+5 = -1$

Subtract from both sides:

$\rightarrow (x+5) - 5 = (-1)-5$

$\rightarrow x = -6$

Which of the following is equivalent to $3^{-2}$ ?

By definition,

$b^{-x} = \frac{1}{b^{x}}$ .

In our problem, and .

Then, we have $\frac{1}{3^{2}} = \frac{1}{9}$ .

Simplify the expression:

$\small (16^{\frac{1}{2}})(256^{\frac{3}{4}})$

Convert the exponent to radical notation.

$x^{\frac{3}{7}}$

Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

$x^{\frac{3}{7}}=\sqrt[7]{x^3}$

Which of the following is equivalent to $64^{\frac{1}{2}}$ ?

By definition, a number raised to the $\frac{1}{2}$ power is the same as the square root of that number.

Since the square root of 64 is 8, 8 is our solution.

Solve for :

$(x+5)^{-3} = -1$

Raise both sides of the equation to the inverse power of to cancel the exponent on the left hand side of the equation.

$\rightarrow ((x+5)^{-3})^{-\frac{1}{3}} = (-1)^{-\frac{1}{3}}$

$\rightarrow x+5 = -1$

Subtract from both sides:

$\rightarrow (x+5) - 5 = (-1)-5$

$\rightarrow x = -6$

Which of the following is equivalent to $3^{-2}$ ?

By definition,

$b^{-x} = \frac{1}{b^{x}}$ .

In our problem, and .

Then, we have $\frac{1}{3^{2}} = \frac{1}{9}$ .

Simplify the expression:

$\small (16^{\frac{1}{2}})(256^{\frac{3}{4}})$

Convert the exponent to radical notation.

$x^{\frac{3}{7}}$

Remember that exponents in the denominator refer to the root of the term, while exponents in the numerator can be treated normally.

$x^{\frac{a}{b}}=\sqrt[b]{x^a}$

$x^{\frac{3}{7}}=\sqrt[7]{x^3}$

Which of the following is equivalent to $64^{\frac{1}{2}}$ ?

By definition, a number raised to the $\frac{1}{2}$ power is the same as the square root of that number.

Since the square root of 64 is 8, 8 is our solution.

Solve for :

$(x+5)^{-3} = -1$

Raise both sides of the equation to the inverse power of to cancel the exponent on the left hand side of the equation.

$\rightarrow ((x+5)^{-3})^{-\frac{1}{3}} = (-1)^{-\frac{1}{3}}$

$\rightarrow x+5 = -1$

Subtract from both sides:

$\rightarrow (x+5) - 5 = (-1)-5$

$\rightarrow x = -6$

Which of the following is equivalent to $3^{-2}$ ?

By definition,

$b^{-x} = \frac{1}{b^{x}}$ .

In our problem, and .

Then, we have $\frac{1}{3^{2}} = \frac{1}{9}$ .