Add or subtract. Assume all variables represent nonnegative real numbers.
-$10 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$
A) $6 x \sqrt [ 4 ] { x ^ { 7 } }$
B) $10 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$
C) $6 x \sqrt [ 4 ] { x ^ { 3 } }$
D) $14 \sqrt [ 4 ] { x ^ { 3 } }$

Question

Quizplus · Accepted Answer

Using the laws of exponents, we can simplify the expression as follows:

\begin{align*}
10 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } } &= 10 x^{7/4} - 4 x \cdot x^{3/4} \
&= 10 x^{7/4} - 4 x^{7/4} \
&= 6 x^{7/4} \
&= 6 \sqrt [ 4 ] { x ^ { 3 } } \cdot \sqrt [ 4 ] { x ^ { 4 } } \
&= 6 x \sqrt [ 4 ] { x ^ { 3 } }.
\end{align*}

Therefore, the best choice is C.

Add or Subtract 10x74−4xx3410 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }104x7​−4x4x3​

Add or Subtract $10 \sqrt [ 4 ] { x ^ { 7 } } - 4 x \sqrt [ 4 ] { x ^ { 3 } }$