Choose the one alternative that best completes the statement or answers the question.
-$16 ( \mathrm { p } / 2 )$ ∙ $\left( \frac { 1 } { 2 } \right) ^ { p }$ ∙ $\left( \frac { 1 } { 2 } \right) ^ { p }$
A) $4 \mathrm { P }$
B) $\left( \frac { 4 } { p } \right) ^ { ( 3 / 2 ) p + 1 }$
C) 1
D) cannot be simplified

Question

Choose the one alternative that best completes the statement or answers the question. 
-$16 ( \mathrm { p } / 2 )$ ∙ $\left( \frac { 1 } { 2 } \right) ^ { p }$ ∙ $\left( \frac { 1 } { 2 } \right) ^ { p }$
A) $4 \mathrm { P }$
B) $\left( \frac { 4 } { p } \right) ^ { ( 3 / 2 ) p + 1 }$
C) 1
D) cannot be simplified

Quizplus · Accepted Answer

The expression simplifies to 1. First, simplify $16 ( \mathrm { p } / 2 )$ to $8p$. Then, combine the powers of $\frac{1}{2}$ by adding the exponents, resulting in $\left( \frac { 1 } { 2 } \right) ^ { 2p }$. The expression becomes $8p \cdot \left( \frac { 1 } { 2 } \right) ^ { 2p }$. Recognizing that $8 = 2^3$, rewrite $8p$ as $(2^3)p$, and then as $2^{3p}$. The entire expression is now $2^{3p} \cdot \left( \frac { 1 } { 2 } \right) ^ { 2p }$, which simplifies to $2^{3p} \cdot 2^{-2p}$. Subtracting the exponents gives $2^{p}$, and since $p$ is the exponent in both the numerator and denominator, they cancel out, leaving the simplified result as 1.

Choose the One Alternative That Best Completes the Statement or Answers