Asked by Justin Chandler on Mar 10, 2024

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Verified

Rewrite the expression using only positive exponents, and simplify. Assume that any variables in the expression are nonzero.
(2a−3b2) 3b(10a4b) 4\frac { \left( 2 a ^ { - 3 } b ^ { 2 } \right) ^ { 3 } b } { \left( 10 a ^ { 4 } b \right) ^ { 4 } }(10a4b) 4(2a3b2) 3b

A) b35a25\frac { b ^ { 3 } } { 5 a ^ { 25 } }5a25b3
B) b31,250a25\frac { b ^ { 3 } } { 1,250 a ^ { 25 } }1,250a25b3
C) b35a24\frac { b ^ { 3 } } { 5 a ^ { 24 } }5a24b3
D) b25a24\frac { b ^ { 2 } } { 5 a ^ { 24 } }5a24b2
E) b21,250a25\frac { b ^ { 2 } } { 1,250 a ^ { 25 } }1,250a25b2

Expression

A combination of variables, numbers, and operations without an equal sign.

A

Often used to denote a variable in equations or to represent a constant value in various mathematical contexts.

  • Employ the characteristics of exponents to condense expressions and resolve equations.
  • Accurately change expressions with negative exponents to forms that have positive exponents.
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Verified Answer

AT
Angelica Touay

Mar 10, 2024

Final Answer :
B
Explanation :
First, simplify the numerator and the denominator separately. For the numerator: (2a−3b2)3⋅b=8a−9b6⋅b=8a−9b7(2a^{-3}b^2)^3 \cdot b = 8a^{-9}b^6 \cdot b = 8a^{-9}b^7(2a3b2)3b=8a9b6b=8a9b7 . For the denominator: (10a4b)4=10,000a16b4(10a^4b)^4 = 10,000a^{16}b^4(10a4b)4=10,000a16b4 . Then, simplify the fraction: 8a−9b710,000a16b4=b31,250a25\frac{8a^{-9}b^7}{10,000a^{16}b^4} = \frac{b^3}{1,250a^{25}}10,000a16b48a9b7=1,250a25b3 , which matches option B.