Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only.
$\left( a ^ { 1 / 5 } a ^ { 1 / 6 } \right) ^ { 30 }$
A) $a ^ { 11 }$
B) $a ^ { 2 }$
C) $30 a ^ { 11 / 30 }$
D) $30 a ^ { 2 }$

Question

Simplify the expression by using the properties of rational exponents. Write the final answer using positive exponents only. 
$\left( a ^ { 1 / 5 } a ^ { 1 / 6 } \right) ^ { 30 }$
A) $a ^ { 11 }$
B) $a ^ { 2 }$
C) $30 a ^ { 11 / 30 }$
D) $30 a ^ { 2 }$

Quizplus · Accepted Answer

When multiplying powers with the same base, you add the exponents. So, $a^{1/5} \cdot a^{1/6} = a^{1/5 + 1/6} = a^{11/30}$. Raising this to the 30th power, $(a^{11/30})^{30} = a^{(11/30) \cdot 30} = a^{11}$.

Simplify the Expression by Using the Properties of Rational Exponents (a1/5a1/6)30\left( a ^ { 1 / 5 } a ^ { 1 / 6 } \right) ^ { 30 }(a1/5a1/6)30

Simplify the Expression by Using the Properties of Rational Exponents $\left( a ^ { 1 / 5 } a ^ { 1 / 6 } \right) ^ { 30 }$