Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$\left( \frac { y ^ { - 8 / 5 } } { b ^ { - 3 / 2 } } \right) ^ { 4 } \left( \frac { b ^ { 1 / 5 } } { y ^ { 1 / 4 } } \right) ^ { - 2 }$$
A) $\frac { \mathrm { y } ^ { 59 / 10 } } { \mathrm {~b} ^ { 28 / 5 } }$
B) $\frac { b ^ { 28 / 5 } } { y ^ { 59 / 10 } }$
C) $\frac { y ^ { 69 / 10 } } { b ^ { 32 / 5 } }$
D) $\frac { b ^ { 32 / 5 } } { y ^ { 69 / 10 } }$

Question

Quizplus · Accepted Answer

First, simplify each part of the expression separately. For the first part, $\left( \frac { y ^ { - 8 / 5 } } { b ^ { - 3 / 2 } } \right) ^ { 4 }$, the exponents are multiplied by 4, resulting in $y^{ - 32 / 5 }$ over $b^{ - 6 }$. For the second part, $\left( \frac { b ^ { 1 / 5 } } { y ^ { 1 / 4 } } \right) ^ { - 2 }$, the exponents are multiplied by -2, resulting in $b^{ - 2 / 5 }$ over $y^{ - 1 / 2 }$. Combining these, you get $y^{ - 32 / 5 + 1 / 2 }$ over $b^{ - 6 - 2 / 5 }$, which simplifies to $y^{ - 59 / 10 }$ over $b^{ - 28 / 5 }$. Flipping the fraction to make the exponents positive gives $b^{ 28 / 5 }$ over $y^{ 59 / 10 }$.

Perform the Indicated Operations (y−8/5b−3/2)4(b1/5y1/4)−2\left( \frac { y ^ { - 8 / 5 } } { b ^ { - 3 / 2 } } \right) ^ { 4 } \left( \frac { b ^ { 1 / 5 } } { y ^ { 1 / 4 } } \right) ^ { - 2 }(b−3/2y−8/5​)4(y1/4b1/5​)−2

Perform the Indicated Operations $\left( \frac { y ^ { - 8 / 5 } } { b ^ { - 3 / 2 } } \right) ^ { 4 } \left( \frac { b ^ { 1 / 5 } } { y ^ { 1 / 4 } } \right) ^ { - 2 }$