Which expression is equivalent to the fraction with numerator open paren 2 5th power of g close paren cubed and denominator open paren 4 h squared close paren cubed ?
Answer
A
the fraction with numerator g 5 and denominator 2 h squared
B
the fraction with numerator 15th power of g and denominator 2 6th power of h
C
the fraction with numerator 15th power of g and denominator 8 6th power of h
D
the fraction with numerator 8th power of g and denominator 8 5th power of h
Explanation
Apply the power of a power rule: (g^5)^3 = g^(5×3) = g^15, and (4h^2)^3 = 4^3h^(2×3) = 64h^6. Since 64 = 2^6, the equivalent fraction is g^15/(2^6h^6), which is choice B.
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