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) $\frac { 1 } { x ^ { 11 / 5 } }$

B) $x ^ { 11 / 5 }$

C) $\frac { 1 } { x ^ { 22 / 7 } }$

D) $x ^ { 22 / 7 }$

Question

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) $\frac { 1 } { x ^ { 11 / 5 } }$

B) $x ^ { 11 / 5 }$

C) $\frac { 1 } { x ^ { 22 / 7 } }$

D) $x ^ { 22 / 7 }$

Quizplus · Accepted Answer

To simplify the expression, use the properties of exponents. For the first fraction, $\frac{x^{1/2}}{(x^2)^{-1/2}}$, apply the power of a power rule to get $x^{1/2} \cdot x^{1}$ which simplifies to $x^{3/2}$. For the second fraction, $\frac{x^{2/5}}{x^{-3/10}}$, add the exponents (since division of like bases involves subtracting exponents and a negative exponent in the denominator is equivalent to a positive exponent in the numerator) to get $x^{4/10 + 3/10} = x^{7/10}$. Multiplying $x^{3/2} \cdot x^{7/10}$ involves adding the exponents, resulting in $x^{15/10 + 7/10} = x^{22/10} = x^{11/5}$.

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