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

Answer:

$(6^{-4})^{-4}=(6^{-2})^{-8}=(6^{8})^{2}=6^{16}$

Step-by-step explanation:

Given: $6^{16}$

We need to correct option equivalent to $6^{16}$

#1 $(6^0)^{16}$

Using exponent property, $(a^m)^n=a^{mn}$

$(6^0)^{16}=6^{0\times 16}\Rightarrow 6^0\neq 6^{16}$

False

#2 $(6^8)^{8}$

Using exponent property, $(a^m)^n=a^{mn}$

$(6^8)^{8}=6^{8\times 8}\Rightarrow 6^{64}\neq 6^{16}$

False

#3 $(6^{-4})^{-4}$

Using exponent property, $(a^m)^n=a^{mn}$

$(6^{-4})^{-4}=6^{-4\times -4}\Rightarrow 6^{16}= 6^{16}$

True

#4 $(6^{-2})^{-8}$

Using exponent property, $(a^m)^n=a^{mn}$

$(6^{-2})^{-8}=6^{-2\times -8}\Rightarrow 6^{16}= 6^{16}$

True

$5 $(6^{-1})^{16}$

Using exponent property, $(a^m)^n=a^{mn}$

$(6^{-1})^{16}=6^{-1\times 16}\Rightarrow 6^{-16}\neq6^{16}$

False

$6 $(6^{8})^{2}$

Using exponent property, $(a^m)^n=a^{mn}$

$(6^{8})^{2}=6^{8\times 2}\Rightarrow 6^{16}= 6^{16}$

True

Hence,   $(6^{-4})^{-4}=(6^{-2})^{-8}=(6^{8})^{2}=6^{16}$