Simplify the following algebraic expression and express your answer using positive exponents only. $\left( 3 x ^ { 6 } y ^ { 7 } \right) ^ { - 5 }$
A) $\frac { 1 } { 243 x ^ { 11 } y ^ { 35 } }$
B) $\frac { 8 } { x ^ { 30 } y ^ { 12 } }$
C) $\frac { 243 } { x ^ { 11 } y ^ { 12 } }$
D) $\frac { 3 } { 243 x ^ { 30 } y ^ { 35 } }$
E) $\frac { 1 } { 243 x ^ { 30 } y ^ { 35 } }$

Question

Quizplus · Accepted Answer

To simplify, we can apply the power of a power rule to the expression inside the parentheses and then apply the power of a product rule to the entire expression. We get:

$\left( 3 x ^ { 6 } y ^ { 7 } \right) ^ { - 5 } = 3^{-5} x^{-6\times 5} y^{-7\times 5} = \frac{1}{243 x^{30} y^{35}}$

Therefore, the best choice is E, which matches the simplified expression.

Simplify the Following Algebraic Expression and Express Your Answer Using (3x6y7)−5\left( 3 x ^ { 6 } y ^ { 7 } \right) ^ { - 5 }(3x6y7)−5

Simplify the Following Algebraic Expression and Express Your Answer Using $\left( 3 x ^ { 6 } y ^ { 7 } \right) ^ { - 5 }$