Use properties of exponents to simplify. $$\left( 9 ^ { 1 + \sqrt { 7 } } \right) \left( 9 ^ { 1 - \sqrt { 7 } } \right)$$
A) 49
B) 81
C) 16
D) $9 \sqrt { 7 }$
E) 343

Question

Quizplus · Accepted Answer

We can use the property of exponents that says when we multiply powers with the same base, we add the exponents. Therefore:

\begin{align*}
\left( 9 ^ { 1 + \sqrt { 7 } } ight) \left( 9 ^ { 1 - \sqrt { 7 } } ight) &= 9^{1+\sqrt{7}+1-\sqrt{7}}\
&= 9^2\
&= 81
\end{align*}

Therefore, the answer is $\boxed{	extbf{(B)}}$.

Use Properties of Exponents to Simplify (91+7)(91−7)\left( 9 ^ { 1 + \sqrt { 7 } } \right) \left( 9 ^ { 1 - \sqrt { 7 } } \right)(91+7​)(91−7​)

Use Properties of Exponents to Simplify $\left( 9 ^ { 1 + \sqrt { 7 } } \right) \left( 9 ^ { 1 - \sqrt { 7 } } \right)$