Question

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

Answer 1

Answer:

1)  $\mathbf{5^{-3}=\frac{1}{125}}$

2)  $\mathbf{-5^{-3}=-\frac{1}{125}}$

3)  $\mathbf{(-5^{-3})^{-1}=-125}$

4)  $\mathbf{(-5^{-3})^0=1}$

Step-by-step explanation:

We need to solve the exponents

1) $5^{-3}$

We know that: $a^{-1}=\frac{1}{a}$

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

So, we get $\mathbf{5^{-3}=\frac{1}{125}}$

2) $-5^{-3}$

We know that: $a^{-1}=\frac{1}{a}$

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

So, we get $\mathbf{-5^{-3}=-\frac{1}{125}}$

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

We know that: $(a^m)^n=a^{m*n}$

Using this rule:

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

So, we get $\mathbf{(-5^{-3})^{-1}=-125}$

4)  $(-5^{-3})^0$

We know that: $(a^m)^n=a^{m*n}$

Using this rule:

$(-5^{-3})^0\\=-5^{-3*0}\\=-5^{0}\\We\:know\:a^0=1\\=1$

So, we get $\mathbf{(-5^{-3})^0=1}$