Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Using the properties of integer exponents, match each expression with its equivalent expression.

Answer 1

From the power rules, the matching of  each expression with its equivalent expression is:

$5^{-3}=\frac{1}{125}$

$-5^{-3}=-\frac{1}{125}$

$(-5^{-3})^{-1}=-125$

$(-5^{-3})^{0}=1$

Power Rules

There are different power rules, see some them:

1. Negative exponent. For this rule when you have a negative exponent, you need to invert the number, i.e, the power base is converted to the denominator. After that, you should solve the power with a positive exponent.  See the  examples:

$4^{-3}=\frac{1}{4^3} =\frac{1}{64} \\ \\ {\frac{4}{6} }^{-2}=( {\frac{6}{4} })^{2}=\frac{36}{16}$

2. Power. For this rule, you should repeat the base and multiply the exponents. See the  example, $(2^{2})^3=2^6=64$.

3. Zero Exponent. When you have an exponent equals to zero, the result must be 1.  See the  example, $2^0=1$.

From this for your question, you have:

• $5^{-3}=\frac{1}{5^3}=\frac{1}{125}$

• $-5^{-3}=-\frac{1}{5^3}=-\frac{1}{125}$

• $(-5^{-3})^{-1}=(-5)^{3}=-125$

• $(-5^{-3})^{0}=(-5)^{0}=1$

Read more about power rules here:

https://brainly.com/question/12140519

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