Question

Use the power of a power property to select each correct way to rewrite the expression. x^15

Answer 1

first, third and fourth

Explanation:

using the rule of exponents

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

then

`(x^3)^(5)` =
`x^(3(5))` =
`x^(15)` ← true

`(x^{(1)/(3))^5 }` =
`x^{(1)/(3)(5) }` =
`x^{(5)/(3) }` ≠
`x^(15)`

`(x^(1)/(3)) ^(45)` =
`x^{(1)/(3)(45) }` =
`x^(15)` ← true

`(x^5)^(3)` =
`x^(5(3))` =
`x^(15)` ← true

`(x^13)^(2)` =
`x^(13(2))` =
`x^(26)` ≠
`x^(15)`

Answer 2

Expressions 1, 3, and 4 all equal
`x^(15)`

Explanation:

See the attached worksheet.