Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

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:

brainly.com/question/12140519

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