Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$\frac { x ^ { 1 / 2 } } { \left( x ^ { 2 } \right) ^ { - 1 / 2 } } \cdot \frac { x ^ { 2 / 5 } } { x ^ { - 3 / 10 } }$
A) $x ^ { 22 / 7 }$
B) $\frac { 1 } { x ^ { 22 / 7 } }$
C) $\frac { 1 } { x ^ { 11 / 5 } }$
D) $x ^ { 11 / 5 }$

Question

Quizplus · Accepted Answer

To simplify the expression, use the properties of exponents: $\frac{x^{a}}{x^{b}} = x^{a-b}$ and $(x^{a})^{b} = x^{ab}$. For the first fraction, $\frac{x^{1/2}}{(x^{2})^{-1/2}} = x^{1/2 - (-1)} = x^{1/2 + 1} = x^{3/2}$. For the second fraction, $\frac{x^{2/5}}{x^{-3/10}} = x^{2/5 + 3/10} = x^{4/10 + 3/10} = x^{7/10}$. Multiplying these results gives $x^{3/2} \cdot x^{7/10} = x^{15/10 + 7/10} = x^{22/10} = x^{11/5}$.

Perform the Indicated Operations x1/2(x2)−1/2⋅x2/5x−3/10\frac { x ^ { 1 / 2 } } { \left( x ^ { 2 } \right) ^ { - 1 / 2 } } \cdot \frac { x ^ { 2 / 5 } } { x ^ { - 3 / 10 } }(x2)−1/2x1/2​⋅x−3/10x2/5​

Perform the Indicated Operations $\frac { x ^ { 1 / 2 } } { \left( x ^ { 2 } \right) ^ { - 1 / 2 } } \cdot \frac { x ^ { 2 / 5 } } { x ^ { - 3 / 10 } }$