Answer:
(B) The exponents should be subtracted by the quotient rule of exponents
Step-by-step explanation:
Let's examine how this was solved.
[tex](\frac{4^2 4^3}{4^{-5}})^2[/tex]
He first rose everything in the parentheses to the second power, which is just multiplying all the exponents by 2. This is correct.
[tex]\frac{4^4 4^6}{4^{-10}}[/tex]
He then combined the numerator exponents. Exponent rules say that [tex]a^b \cdot a^c = a^b+c[/tex], so he should have ended up with [tex]4^{10}[/tex], which he did. This is correct.
[tex]\frac{4^{10}}{4^{-10}}[/tex]
Now, what he did in the final step is wrong. He added the exponents. However, exponent rules tell us that when we have [tex]\frac{a^b}{a^c}[/tex], it equals [tex]a^{b-c}[/tex].
[tex]10 - (-10) = 10+10 = 20[/tex]
So the final answer should have been [tex]4^{20}[/tex]
Hope this helped!
