Question

1. an expression is given.

\frac{(2^{4})^{2}\cdot2^{7}}{2^{6}}
select all the expressions that are equivalent to the given expression.
\textcircled{a}\frac{2^{15}}{2^{6}}
\textcircled{b}2^{21}
\textcircled{c}2^{11}
\textcircled{d}2^{9}
\textcircled{e}\frac{2^{13}}{2^{6}}

Explanation:

Step1: Simplify the numerator's first - part

Use the power - of - a - power rule \((a^m)^n=a^{mn}\). For \((2^4)^2\), we have \((2^4)^2 = 2^{4\times2}=2^8\).

Step2: Simplify the numerator

Use the product rule \(a^m\times a^n=a^{m + n}\). The numerator \(2^8\times2^7=2^{8 + 7}=2^{15}\).

Step3: Simplify the whole expression

Use the quotient rule \(a^m\div a^n=a^{m - n}\). The original expression \(\frac{2^{15}}{2^6}=2^{15-6}=2^9\).

Answer:

A. \(\frac{2^{15}}{2^6}\), D. \(2^9\)