Understanding Negative Exponents

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Math › Understanding Negative Exponents

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1

Solve for :

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

CORRECT

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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:

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

$\rightarrow x = -6$

2

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

$\frac{1}{9}$

CORRECT

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$\frac{1}{6}$

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Explanation

By definition,

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

In our problem, and .

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

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