Raise to indicated power and simplify: $\left( 2 x ^ { \frac { 3 } { 4 } } y ^ { 2 } \right) ^ { 4 }$
A) $16 x^ 3 y 8$
B) $16 x ^ { \frac { 19 } { 4 } } y ^ { 6 }$
C) $2 x ^3 y^ 2$
D) $8 x ^ { 3 } y ^ { 8 }$

Question

Raise to indicated power and simplify: $\left( 2 x ^ { \frac { 3 } { 4 } } y ^ { 2 } \right) ^ { 4 }$
A) $16 x^ 3 y 8$ 
B) $16 x ^ { \frac { 19 } { 4 } } y ^ { 6 }$ 
C) $2 x ^3 y^ 2$ 
D) $8 x ^ { 3 } y ^ { 8 }$

Quizplus · Accepted Answer

When raising a power to a power, you multiply the exponents. For $2x^{\frac{3}{4}}y^2$ raised to the 4th power, the exponent of $x$ becomes $\frac{3}{4} \times 4 = 3$ and the exponent of $y$ becomes $2 \times 4 = 8$. The coefficient $2$ raised to the 4th power is $2^4 = 16$, resulting in $16x^3y^8$.

Raise to Indicated Power and Simplify (2x34y2)4\left( 2 x ^ { \frac { 3 } { 4 } } y ^ { 2 } \right) ^ { 4 }(2x43​y2)4

Raise to Indicated Power and Simplify $\left( 2 x ^ { \frac { 3 } { 4 } } y ^ { 2 } \right) ^ { 4 }$