Which expression is equivalent to 5 r to the 6th power t to the 4th power open paren the fraction with numerator 4 r cubed s squared t to the 4th power and denominator 2 r to the 4th power st to the 6th power close paren to the 5th power ?
Answer
A
the fraction with numerator 160 r s to the 5th power and denominator t to the 6th power
B
the fraction with numerator 50 r s to the 5th power and denominator t to the 6th power
C
the fraction with numerator 160 s to the 6th power and denominator t cubed
D
the fraction with numerator 50 s to the 6th power and denominator t cubed
Explanation
First simplify the fraction inside the parentheses: (4r³s²t⁴)/(2r⁴st⁶) = 2s/(rt²). Raising this to the fifth power gives 32s⁵/(r⁵t¹⁰). Multiplying by 5r⁶t⁴ gives 160rs⁵/t⁶, which matches the choice with numerator 160rs⁵ and denominator t⁶.
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