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

5-3 -----> 1/125

-5-3 ------> -1/125

(-5-3)-1 -------> -125

(-5-3)0 --------> 1

Explanation:

The other person is correct but i simplified it a little bit.

Answer 2

(a)

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

(b)

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

(c)

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

(d)

`(-5^(-3))^(0)=1`

Explanation:

(a)

`5^(-3)`

we can use property of exponent

`a^(-n)=(1)/(a^n)`

we get

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

`5^(-3)=(1)/(5* 5* 5)`

`5^(-3)=(1)/(125)`........Answer

(b)

`-5^(-3)`

we can use property of exponent

`a^(-n)=(1)/(a^n)`

we get

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

`-5^(-3)=-(1)/(5* 5* 5)`

`-5^(-3)=-(1)/(125)`........Answer

(c)

`(-5^(-3))^(-1)`

we can use property of exponent

`(a^(n))^m=a^(m* n)`

we get

`(-5^(-3))^(-1)=(-5)^(-3* -1)`

`(-5^(-3))^(-1)=(-5)^3`

`(-5^(-3))^(-1)=(-5)* (-5)* (-5)`

`(-5^(-3))^(-1)=-125`........Answer

(d)

`(-5^(-3))^(0)`

we can use property of exponent

`(a^(n))^m=a^(m* n)`

we get

`(-5^(-3))^(0)=(-5)^(-3* 0)`

`(-5^(-3))^(-1)=(-5)^0`

we can use property

`a^0=1`

`(-5^(-3))^(0)=1`........Answer