Rewrite the expression using only positive exponents, and simplify. Assume that any variables in the expression are nonzero.
$4\frac { \left( 2 a ^ { - 3 } b ^ { 2 } \right) ^ { 3 } b } { \left( 10 a ^ { 4 } b \right) ^ { 4 } }$

A) $b35a25\frac { b ^ { 3 } } { 5 a ^ { 25 } }$
B) $b31,250a25\frac { b ^ { 3 } } { 1,250 a ^ { 25 } }$
C) $b35a24\frac { b ^ { 3 } } { 5 a ^ { 24 } }$
D) $b25a24\frac { b ^ { 2 } } { 5 a ^ { 24 } }$
E) $b21,250a25\frac { b ^ { 2 } } { 1,250 a ^ { 25 } }$

Question

Rewrite the expression using only positive exponents, and simplify. Assume that any variables in the expression are nonzero.

4\frac { \left( 2 a ^ { - 3 } b ^ { 2 } \right) ^ { 3 } b } { \left( 10 a ^ { 4 } b \right) ^ { 4 } }

A)

b35a25\frac { b ^ { 3 } } { 5 a ^ { 25 } }

B)

b31,250a25\frac { b ^ { 3 } } { 1,250 a ^ { 25 } }

C)

b35a24\frac { b ^ { 3 } } { 5 a ^ { 24 } }

D)

b25a24\frac { b ^ { 2 } } { 5 a ^ { 24 } }

E)

b21,250a25\frac { b ^ { 2 } } { 1,250 a ^ { 25 } }

Angelica Touay · Accepted Answer

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

Definitions

Learning Objectives

Learning Objectives

Related questions