Which is the simplified form of open paren the fraction with numerator 2 A b and denominator A to the negative 5 power b squared close paren to the negative 3 power ? Assume A is not equal to 0 , b is not equal to 0
Answer
A
the fraction with numerator 2 A to the 6th power and denominator b to the 5th power
B
the fraction with numerator b squared and denominator 8 A to the 45th power
C
the fraction with numerator b cubed and denominator 8 A to the 18th power
D
the fraction with numerator A to the 6th power and denominator 4 b
Explanation
First simplify inside the parentheses: dividing by A⁻⁵ is the same as multiplying by A⁵, so the expression becomes (2A⁶/b)⁻³. A negative exponent means take the reciprocal, giving (b/(2A⁶))³. Cubing the numerator and denominator gives b³/(8A¹⁸), which is choice C.
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