Rewrite without rational exponents, and simplify, if possible.
-$\left( 9 y ^ { 8 } \right) ^ { 3 / 2 }$
A) $27 y ^ { 3 / 2 }$
B) $9 y ^ { 24 }$
C) $27 \mathrm { y } ^ { 12 }$
D) $27 ^ { 17 }$

Question

Quizplus · Accepted Answer

To rewrite $\left( 9 y ^ { 8 } \right) ^ { 3 / 2 }$ without rational exponents and simplify, we apply the rule $(a^m)^n = a^{mn}$ to both the coefficient and the variable part. For the coefficient $9^{3/2}$, we find the square root of 9 (which is 3) and then raise it to the power of 3, resulting in $3^3 = 27$. For the variable part $y^{8 \cdot 3/2}$, we multiply the exponents to get $y^{12}$. Therefore, the simplified expression is $27y^{12}$.

Rewrite Without Rational Exponents, and Simplify, If Possible (9y8)3/2\left( 9 y ^ { 8 } \right) ^ { 3 / 2 }(9y8)3/2

Rewrite Without Rational Exponents, and Simplify, If Possible $\left( 9 y ^ { 8 } \right) ^ { 3 / 2 }$