Question

Does anyone know the answer to this?

Answer 1

(B) The exponents should be subtracted by the quotient rule of exponents

Explanation:

Let's examine how this was solved.

`((4^2 4^3)/(4^(-5)))^2`

He first rose everything in the parentheses to the second power, which is just multiplying all the exponents by 2. This is correct.

`(4^4 4^6)/(4^(-10))`

He then combined the numerator exponents. Exponent rules say that
`a^b \cdot a^c = a^b+c`, so he should have ended up with
`4^(10)`, which he did. This is correct.

`(4^(10))/(4^(-10))`

Now, what he did in the final step is wrong. He added the exponents. However, exponent rules tell us that when we have
`(a^b)/(a^c)`, it equals
`a^(b-c)`.

`10 - (-10) = 10+10 = 20`

So the final answer should have been
`4^(20)`

Hope this helped!