Question

Math 171

-5^2 times (3/5)^3

Answer 1

(−52)((−35)3)

=−25(−35)3

=−25(−27/125)

=27/5

Answer 2

`(-5)^2*((3)/(5))^3=(27)/(5)`

Explanation:

`(-5)^2*((3)/(5))^3`

Using , property of exponents,

`(ab)^x=a^x* b^x`

=
`(-1)^2*(5)^2*((3^3)/(5^3))`

Using , property of exponents,

`(a^x)/(a^y)=a^(x-y)`

=
`(5)^(2-3)*{3}^3`

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

Using , property of exponents,

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

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

=
`(3*3*3)/(5)`

=
`(27)/(5)`

Thus,
`(-5)^2*((3)/(5))^3=(27)/(5)`