Rewrite the expression using only positive exponents, and simplify. Assume that any variables in the expression are nonzero.
$\frac { \left( 2 a ^ { - 3 } b ^ { 2 } \right) ^ { 3 } b } { \left( 10 a ^ { 4 } b \right) ^ { 4 } }$
A) $\frac { b ^ { 3 } } { 5 a ^ { 25 } }$
B) $\frac { b ^ { 3 } } { 1,250 a ^ { 25 } }$
C) $\frac { b ^ { 3 } } { 5 a ^ { 24 } }$
D) $\frac { b ^ { 2 } } { 5 a ^ { 24 } }$
E) $\frac { b ^ { 2 } } { 1,250 a ^ { 25 } }$

Question

Rewrite the expression using only positive exponents, and simplify. Assume that any variables in the expression are nonzero. 
$\frac { \left( 2 a ^ { - 3 } b ^ { 2 } \right) ^ { 3 } b } { \left( 10 a ^ { 4 } b \right) ^ { 4 } }$
A) $\frac { b ^ { 3 } } { 5 a ^ { 25 } }$
B) $\frac { b ^ { 3 } } { 1,250 a ^ { 25 } }$
C) $\frac { b ^ { 3 } } { 5 a ^ { 24 } }$
D) $\frac { b ^ { 2 } } { 5 a ^ { 24 } }$
E) $\frac { b ^ { 2 } } { 1,250 a ^ { 25 } }$

Quizplus · Accepted Answer

First, simplify the numerator and the denominator separately. For the numerator: $(2a^{-3}b^2)^3 \cdot b = 8a^{-9}b^6 \cdot b = 8a^{-9}b^7$. For the denominator: $(10a^4b)^4 = 10,000a^{16}b^4$. Then, simplify the fraction: $\frac{8a^{-9}b^7}{10,000a^{16}b^4} = \frac{b^3}{1,250a^{25}}$, which matches option B.

Rewrite the Expression Using Only Positive Exponents, and Simplify (2a−3b2)3b(10a4b)4\frac { \left( 2 a ^ { - 3 } b ^ { 2 } \right) ^ { 3 } b } { \left( 10 a ^ { 4 } b \right) ^ { 4 } }(10a4b)4(2a−3b2)3b​

Rewrite the Expression Using Only Positive Exponents, and Simplify $\frac { \left( 2 a ^ { - 3 } b ^ { 2 } \right) ^ { 3 } b } { \left( 10 a ^ { 4 } b \right) ^ { 4 } }$