Use rational exponents to write as a single radical expression.
-$$\sqrt [ 4 ] { 4 } \cdot \sqrt [ 3 ] { x }$$
A) $\sqrt [ 12 ] { 64 x ^ { 4 } }$
B) $\sqrt [ 12 ] { 4 x }$
C) $\sqrt [ 12 ] { 4 x ^ { 4 } }$
D) $\sqrt [ 4 ] { 4 x }$

Question

Quizplus · Accepted Answer

The expression $\sqrt [ 4 ] { 4 } \cdot \sqrt [ 3 ] { x }$ can be written using rational exponents as $4^{1/4} \cdot x^{1/3}$. To combine these into a single radical expression, find a common denominator for the exponents, which is 12. This gives $4^{3/12} \cdot x^{4/12}$, or $4^3 \cdot x^4$ under a single radical with an index of 12, resulting in $\sqrt [ 12 ] { 64 x ^ { 4 } }$.

Use Rational Exponents to Write as a Single Radical Expression 44⋅x3\sqrt [ 4 ] { 4 } \cdot \sqrt [ 3 ] { x }44​⋅3x​

Use Rational Exponents to Write as a Single Radical Expression $\sqrt [ 4 ] { 4 } \cdot \sqrt [ 3 ] { x }$