Question

Using the properties of Integer exponents, match each expression with its equivalent expression.

Answer 1

The -5⁻³ matches with -1/125, (-5⁻³)⁻¹ matches with -125, and (-5⁻³)⁰ matches with 1.

What is integer exponent?

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

5⁻³ = 1/5³ = 1/125

-5⁻³ = -1/5³ = -1/125

(-5⁻³)⁻¹ = (-1/5³)⁻¹ = (-1/125)⁻¹ = -125

(-5⁻³)⁰ = 1   $\rm (a^0 = 1)$

Thus, the -5⁻³ matches with -1/125, (-5⁻³)⁻¹ matches with -125, and (-5⁻³)⁰ matches with 1.

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Answer 2

Answer:

$\sf{1)\ 5^{-3}={\dfrac{1}{5^3}={\dfrac{1}{125}$

$\sf{2)\ -5^{-3}={\dfrac{1}{-5^3}=-{\dfrac{1}{125}$

$\sf{3)\ \left(-5^{-3}\right)^{-1}=\left(-5^{-3\times-1}\right)=-5^{3}=-125}$

$\sf{4)\ \left(-5^{-3}\right)^{0}=1$

Step-by-step explanation:

Exponent Property Rules:

⟹ Zero Exponent Property - ex: x⁰ = 1

An integer (excluding 0) with an exponent of zero equals one.

⟹ Negative Exponent Property - ex: x⁻ⁿ = ${\dfrac{1}{x^n}$

Any number raised to a negative power is equivalent to the reciprocal of the number's positive exponent.

⟹ Power of Product Property - ex: (xy)ⁿ = xⁿ × yⁿ

To find the power of a product, multiply the power of each factor.

$\sf{1)\ 5^{-3}={\dfrac{1}{5^3}={\dfrac{1}{125}$

$\sf{2)\ -5^{-3}={\dfrac{1}{-5^3}=-{\dfrac{1}{125}$

$\sf{3)\ \left(-5^{-3}\right)^{-1}=\left(-5^{-3\times-1}\right)=-5^{3}=-125}$

$\sf{4)\ \left(-5^{-3}\right)^{0}=1$

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