Use the properties of exponents to simplify the expression. Write with positive exponents.
-$\frac { x ^ { - 1 / 2 } y ^ { 3 / 8 } } { \left( x ^ { 4 } y ^ { - 5 } \right) ^ { - 1 / 2 } }$
A) $x ^ { 3 / 2 } y ^ { 17 / 8 }$
B) $\frac { y ^ { 17 / 8 } } { x ^ { 3 / 2 } }$
C) $\frac { x ^ { 3 / 2 } } { y ^ { 17 / 8 } }$
D) $- \frac { x ^ { 3 / 2 } } { y ^ { 17 / 8 } }$

Question

Quizplus · Accepted Answer

To simplify the expression, apply the properties of exponents. First, distribute the exponent $-1/2$ across $x^4$ and $y^{-5}$ in the denominator. This gives $x^{-1/2}y^{3/8}$ over $x^{-2}y^{5/2}$. Then, combine the exponents for $x$ and $y$ by subtracting the exponents in the denominator from those in the numerator, resulting in $x^{3/2}$ and $y^{-17/8}$. Finally, rewrite $y^{-17/8}$ with a positive exponent in the denominator to get $\frac{x^{3/2}}{y^{17/8}}$.

Use the Properties of Exponents to Simplify the Expression x−1/2y3/8(x4y−5)−1/2\frac { x ^ { - 1 / 2 } y ^ { 3 / 8 } } { \left( x ^ { 4 } y ^ { - 5 } \right) ^ { - 1 / 2 } }(x4y−5)−1/2x−1/2y3/8​

Use the Properties of Exponents to Simplify the Expression $\frac { x ^ { - 1 / 2 } y ^ { 3 / 8 } } { \left( x ^ { 4 } y ^ { - 5 } \right) ^ { - 1 / 2 } }$