Understanding Fractional Exponents - Math

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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.

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

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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.

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

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

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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.

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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

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

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

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Understanding Fractional 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.

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.

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.

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.

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.

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.

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.

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.