Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers.
-$$\left( 9 x ^ { 16 } y ^ { - 18 } \right) ^ { 5 / 2 }$$
A) $\frac { 243 x ^ { 40 } } { y ^ { 45 } }$
B) $243 x ^ { 40 } y ^ { 45 }$
C) $\frac { 9 x ^ { 40 } } { y ^ { 45 } }$
D) $\frac { 243 } { \mathrm { x } ^ { 40 } \mathrm { y } ^ { 45 } }$

Question

Quizplus · Accepted Answer

To simplify the expression $\left( 9 x ^ { 16 } y ^ { - 18 } \right) ^ { 5 / 2 }$, first apply the exponent $5/2$ to each factor inside the parentheses. For $9^{5/2}$, since $9 = 3^2$, it becomes $(3^2)^{5/2} = 3^5 = 243$. For $x^{16}$, it becomes $x^{(16)(5/2)} = x^{40}$. For $y^{-18}$, it becomes $y^{(-18)(5/2)} = y^{-45}$, which when written with a positive exponent becomes $\frac{1}{y^{45}}$. Combining these results gives $\frac{243 x^{40}}{y^{45}}$.

Simplify the Exponential Expression (9x16y−18)5/2\left( 9 x ^ { 16 } y ^ { - 18 } \right) ^ { 5 / 2 }(9x16y−18)5/2

Simplify the Exponential Expression $\left( 9 x ^ { 16 } y ^ { - 18 } \right) ^ { 5 / 2 }$