Question

Which expressions are equivalent to 6^16? Check all that apply. (6^8)^2 is the last answer.

Answer 1

The fourth and last are correct.

One you have and exponent of an exponent, the base stays the same and the exponents get to be multiplyied:

`\bf~(y^(x))^(z) = y^(xz)`

Both -8 x -2 and 8 x 2 equal 16.

Answer:

`\boxed{\bf~The~fourth~and~last~options~are~correct.}`

Hope it helped,

Happy homework/ study/ exam!

Answer 2

`(6^(-4))^(-4)=(6^(-2))^(-8)=(6^(8))^(2)=6^(16)`

Explanation:

Given:
`6^(16)`

We need to correct option equivalent to
`6^(16)`

#1
`(6^0)^(16)`

Using exponent property,
`(a^m)^n=a^(mn)`

`(6^0)^(16)=6^(0* 16)\Rightarrow 6^0\\eq 6^(16)`

False

#2
`(6^8)^(8)`

Using exponent property,
`(a^m)^n=a^(mn)`

`(6^8)^(8)=6^(8* 8)\Rightarrow 6^(64)\\eq 6^(16)`

False

#3
`(6^(-4))^(-4)`

Using exponent property,
`(a^m)^n=a^(mn)`

`(6^(-4))^(-4)=6^(-4* -4)\Rightarrow 6^(16)= 6^(16)`

True

#4
`(6^(-2))^(-8)`

Using exponent property,
`(a^m)^n=a^(mn)`

`(6^(-2))^(-8)=6^(-2* -8)\Rightarrow 6^(16)= 6^(16)`

True

$5
`(6^(-1))^(16)`

Using exponent property,
`(a^m)^n=a^(mn)`

`(6^(-1))^(16)=6^(-1* 16)\Rightarrow 6^(-16)\\eq6^(16)`

False

$6
`(6^(8))^(2)`

Using exponent property,
`(a^m)^n=a^(mn)`

`(6^(8))^(2)=6^(8* 2)\Rightarrow 6^(16)= 6^(16)`

True

Hence,
`(6^(-4))^(-4)=(6^(-2))^(-8)=(6^(8))^(2)=6^(16)`