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High School Math : Understanding Negative Exponents

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Example Questions

Example Question #1 : Exponents

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

Possible Answers:

$\frac{1}{6}$ $\displaystyle \frac{1}{6}$

$\displaystyle -6$

$\frac{1}{9}$ $\displaystyle \frac{1}{9}$

$\displaystyle -9$

$\displaystyle 1$

Correct answer:

$\frac{1}{9}$ $\displaystyle \frac{1}{9}$

Explanation:

By definition,

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

In our problem, b = 3 $\displaystyle b = 3$ and x = 2 $\displaystyle x = 2$.

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

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Example Question #1 : Negative Exponents

Solve for $\displaystyle x$:

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

Possible Answers:

$\displaystyle -5$

$\displaystyle -6$

$\displaystyle -1$

$\displaystyle -4$

$\displaystyle -3$

Correct answer:

$\displaystyle -6$

Explanation:

Raise both sides of the equation to the inverse power of $\displaystyle -3$ to cancel the exponent on the left hand side of the equation.

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

$\rightarrow x+5 = -1$ $\displaystyle \rightarrow x+5 = -1$

Subtract $\displaystyle 5$ from both sides:

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

$\rightarrow x = -6$ $\displaystyle \rightarrow x = -6$

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High School Math : Understanding Negative Exponents

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Exponents

Example Question #1 : Negative Exponents

All High School Math Resources

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