Question

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

Answer 1

1)
`\mathbf{5^(-3)=(1)/(125)}`

2)
`\mathbf{-5^(-3)=-(1)/(125)}`

3)
`\mathbf{(-5^(-3))^(-1)=-125}`

4)
`\mathbf{(-5^(-3))^0=1}`

Explanation:

We need to solve the exponents

1)
`5^(-3)`

We know that:
`a^(-1)=(1)/(a)`

`5^(-3)\\=(1)/(5^3)\\=(1)/(125)`

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

2)
`-5^(-3)`

We know that:
`a^(-1)=(1)/(a)`

`-5^(-3)\\=-(1)/(5^3)\\=-(1)/(125)`

So, we get
`\mathbf{-5^(-3)=-(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}`