Simplify the expression. $\left( \frac { 5 x ^ { - 5 } y ^ { 5 } z ^ { - 7 } } { 20 x ^ { 6 } y ^ { 10 } z ^ { - 12 } } \right) ^ { 3 }$ Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined.
A)$\frac { z ^ { 5 } } { 4 x ^ { 33 } y ^ { 15 } }$
B)
$\frac { z ^ { 15 } } { 64 x ^ { 33 } y ^ { 15 } }$
C) $\quad \frac { z ^ { 15 } } { 64 x ^ { 15 } y ^ { 33 } }$
D)$\frac { z ^ { 5 } } { 4 x ^ { 11 } y ^ { 5 } }$
E)$\frac { z ^ { 15 } } { 64 x ^ { - 33 } y ^ { - 15 } }$

Question

Simplify the expression. $\left( \frac { 5 x ^ { - 5 } y ^ { 5 } z ^ { - 7 } } { 20 x ^ { 6 } y ^ { 10 } z ^ { - 12 } } \right) ^ { 3 }$ Write the answer without using negative exponents. Assume that all variables are restricted to those numbers for which the expression is defined. 
A)$\frac { z ^ { 5 } } { 4 x ^ { 33 } y ^ { 15 } }$
B)
$\frac { z ^ { 15 } } { 64 x ^ { 33 } y ^ { 15 } }$
C) $\quad \frac { z ^ { 15 } } { 64 x ^ { 15 } y ^ { 33 } }$
D)$\frac { z ^ { 5 } } { 4 x ^ { 11 } y ^ { 5 } }$
E)$\frac { z ^ { 15 } } { 64 x ^ { - 33 } y ^ { - 15 } }$

Quizplus · Accepted Answer

First, simplify the expression inside the parentheses by subtracting the exponents of like bases in the numerator from those in the denominator: $5x^{-5-6}y^{5-10}z^{-7-(-12)} = \frac{5}{20}x^{-11}y^{-5}z^{5}$. Simplifying the fraction $\frac{5}{20} = \frac{1}{4}$, we get $\frac{1}{4}x^{-11}y^{-5}z^{5}$. Raising this to the third power, we get $\left(\frac{1}{4}\right)^3x^{-33}y^{-15}z^{15} = \frac{1}{64}x^{-33}y^{-15}z^{15}$, which, when rewritten without negative exponents, gives $\frac{z^{15}}{64x^{33}y^{15}}$.

Simplify the Expression (5x−5y5z−720x6y10z−12)3\left( \frac { 5 x ^ { - 5 } y ^ { 5 } z ^ { - 7 } } { 20 x ^ { 6 } y ^ { 10 } z ^ { - 12 } } \right) ^ { 3 }(20x6y10z−125x−5y5z−7​)3

Simplify the Expression $\left( \frac { 5 x ^ { - 5 } y ^ { 5 } z ^ { - 7 } } { 20 x ^ { 6 } y ^ { 10 } z ^ { - 12 } } \right) ^ { 3 }$