Maths-
SAT
Easy

Question

If fraction numerator square root of x to the power of 5 end root over denominator cube root of x to the power of 4 end root end fraction equals x to the power of a over b end exponent for all positive values of x, what is the value of a over b?

The correct answer is: 7/6


    fraction numerator square root of x to the power of 5 end root over denominator cube root of x to the power of 4 end root end fraction equals x to the power of a over b end exponent
    rightwards double arrow x to the power of 5 over 2 end exponent over x to the power of 4 over 3 end exponent equals x to the power of 5 over 2 minus 4 over 3 end exponent equals x to the power of fraction numerator 5 cross times 3 minus 4 cross times 2 over denominator 6 end fraction end exponent equals x to the power of fraction numerator 15 minus 8 over denominator 6 end fraction end exponent equals x to the power of 7 over 6 end exponent equals x to the power of a over b end exponent
    a = 7, b = 6
    a over b equals 7 over 6 equals 1.166

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