Simplify the expression. $8 ^ { \sqrt { 5 } } \cdot 8 ^ { \sqrt { 5 } }$
A) $\quad 8 \sqrt { 10 }$
B) $\quad 16 ^ { \sqrt { 10 } }$
C) $\quad 5 ^ { \sqrt { 8 } }$
D) $\quad 64 \sqrt { 5 }$
E) $\quad 64 \sqrt { 10 }$

Question

Quizplus · Accepted Answer

When you multiply two exponents with the same base, you add their exponents. Therefore,

$8 ^ { \sqrt { 5 } } \cdot 8 ^ { \sqrt { 5 } } = 8 ^ { \sqrt { 5 } + \sqrt { 5 } } = 8 ^ { 2\sqrt { 5 } }$

To simplify further, we can write $8$ as $2^3$. Then,

$8 ^ { 2\sqrt { 5 } } = (2^3) ^ { 2\sqrt { 5 } } = 2 ^ { 6\sqrt { 5 } }$

Finally, we can write $2 ^ { 6\sqrt { 5 } }$ as $64\sqrt{5}$, so the answer is D.

Simplify the Expression 85⋅858 ^ { \sqrt { 5 } } \cdot 8 ^ { \sqrt { 5 } }85​⋅85​

Simplify the Expression $8 ^ { \sqrt { 5 } } \cdot 8 ^ { \sqrt { 5 } }$