Simplify. Write the answer using positive exponents only.
-$\frac { \left( 5 x y ^ { 3 } z ^ { - 3 } \right) ^ { 3 } } { \left( 2 x ^ { 5 } y z ^ { - 3 } \right) ^ { - 1 } }$
A) $\frac { 250 x ^ { 8 } y ^ { 10 } } { z ^ { 12 } }$
B) - $\frac { 125 x ^ { 8 } y ^ { 10 } } { 2 z ^ { 12 } }$
C)- $\frac { 125 y ^ { 10 } } { 2 x ^ { 2 } z ^ { 12 } }$
D) $\frac { 250 y ^ { 10 } } { x ^ { 4 } z ^ { 12 } }$

Question

Quizplus · Accepted Answer

First, apply the power to each term inside the parentheses. For the numerator, $ (5^3)(x^3)(y^{3*3})(z^{-3*3}) = 125x^3y^9z^{-9} $. For the denominator, since it's raised to the power of -1, it inverts the fraction and changes the sign of the exponent, resulting in $2x^{-5}y^{-1}z^3$. Multiplying these together, you get $ \frac{125x^3y^9z^{-9}}{2x^{-5}y^{-1}z^3} = \frac{125}{2}x^{3-(-5)}y^{9-(-1)}z^{-9-3} = \frac{250x^8y^{10}}{z^{12}} $.

Simplify Write the Answer Using Positive Exponents Only (5xy3z−3)3(2x5yz−3)−1\frac { \left( 5 x y ^ { 3 } z ^ { - 3 } \right) ^ { 3 } } { \left( 2 x ^ { 5 } y z ^ { - 3 } \right) ^ { - 1 } }(2x5yz−3)−1(5xy3z−3)3​

Simplify Write the Answer Using Positive Exponents Only $\frac { \left( 5 x y ^ { 3 } z ^ { - 3 } \right) ^ { 3 } } { \left( 2 x ^ { 5 } y z ^ { - 3 } \right) ^ { - 1 } }$