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High School Math : Understanding Exponents

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Example Questions

Example Question #1 : Understanding Negative Exponents

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

Possible Answers:

$\frac{1}{6}$

$\frac{1}{9}$

Correct answer:

$\frac{1}{9}$

Explanation:

By definition,

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

In our problem, b = 3 and x = 2 .

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

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Example Question #3 : Negative Exponents

Solve for :

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

Possible Answers:

Correct answer:

Explanation:

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:

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

$\rightarrow x = -6$

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Example Question #2 : Fractional Exponents

Convert the exponent to radical notation.

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

Possible Answers:

$\small \small \sqrt[3]{x^7}$

$\small \frac{1}{x^4}$

$\small \small \sqrt[7]{x^3}$

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

Correct answer:

$\small \small \sqrt[7]{x^3}$

Explanation:

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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Example Question #1 : Understanding Exponents

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

Possible Answers:

$\frac{1}{32}$

Correct answer:

Explanation:

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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Example Question #1 : Fractional Exponents

Simplify the expression:

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

Possible Answers:

1024

256

Correct answer:

256

Explanation:

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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High School Math : Understanding Exponents

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Understanding Negative Exponents

Example Question #3 : Negative Exponents

Example Question #2 : Fractional Exponents

Example Question #1 : Understanding Exponents

Example Question #1 : Fractional Exponents

All High School Math Resources

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