Use the laws of exponents to simplify. Do not use negative exponents in your answer.
-$$\frac { 81 ^ { 5 } \cdot 3 ^ { - 3 } } { 9 ^ { 5 } }$$
A) $3 ^ { 7 }$
B) $3 ^ { 5 }$
C) $9 ^ { 7 }$
D) 1

Question

Quizplus · Accepted Answer

First, we can simplify 81 to 3 raised to the 4th power: $81=3^4$
Therefore, we have $\frac{(3^4)^5 \cdot 3^{-3}}{9^5}$, which simplifies to $\frac{3^{20} \cdot 3^{-3}}{9^5}$. 
We can then simplify the denominator by noting that $9$ is equal to $3^2$: $9=3^2$. Therefore, $9^5$ is equal to $3^{10}$.
Substituting this in, we have $\frac{3^{20} \cdot 3^{-3}}{3^{10}}$. 
Combining the exponents of the numerator terms, we get $3^{20-3}=3^{17}$. Dividing by $3^{10}$, we get $3^{7}$ as our final answer.

Use the Laws of Exponents to Simplify 815⋅3−395\frac { 81 ^ { 5 } \cdot 3 ^ { - 3 } } { 9 ^ { 5 } }95815⋅3−3​

Use the Laws of Exponents to Simplify $\frac { 81 ^ { 5 } \cdot 3 ^ { - 3 } } { 9 ^ { 5 } }$