Rewrite without rational exponents, and simplify, if possible.
-$( 16 x ) ^ { 7 / 2 }$
A) $2 \sqrt { 8 x }$
B) $16,384 \sqrt { \mathrm { x } ^ { 14 } }$
C) $16,384 x ^ { 3 } \sqrt { x }$
D) $128 \sqrt { x }$

Question

Quizplus · Accepted Answer

To rewrite $(16x)^{7/2}$ without rational exponents and simplify, we first break it down into its components. The expression can be seen as $(16)^{7/2} \cdot (x)^{7/2}$. The term $(16)^{7/2}$ simplifies to $16^{3.5}$ or $16^3 \cdot 16^{0.5}$, which equals $4096 \cdot 4 = 16384$. The term $(x)^{7/2}$ simplifies to $x^3 \cdot x^{0.5}$ or $x^3 \sqrt{x}$. Combining these, we get $16384 x^3 \sqrt{x}$.

Rewrite Without Rational Exponents, and Simplify, If Possible (16x)7/2( 16 x ) ^ { 7 / 2 }(16x)7/2

Rewrite Without Rational Exponents, and Simplify, If Possible $( 16 x ) ^ { 7 / 2 }$