Question

Does anyone know the answer to this?

Answer 1

Answer:

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

Step-by-step explanation:

Let's examine how this was solved.

$(\frac{4^2 4^3}{4^{-5}})^2$

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

$\frac{4^4 4^6}{4^{-10}}$

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.

$\frac{4^{10}}{4^{-10}}$

Now, what he did in the final step is wrong. He added the exponents. However, exponent rules tell us that when we have $\frac{a^b}{a^c}$, it equals $a^{b-c}$.

$10 - (-10) = 10+10 = 20$

So the final answer should have been $4^{20}$

Hope this helped!