Question

If the expression below is equal to yᵃ for all positive values of y, what is the value of a?

Answer 1

y^5/12

Explanation:

y ^ 1/4 * y ^ 1/2

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y ^ 1/3

We know a^b * a^c = a^(b+c)

y^ 1/4 * y^1/2 = y^ (1/4+1/2) = y^(1/4+2/4) = y^(3/4)

y ^ 3/4

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y ^ 1/3

We know a^b / a^c = y(b-c)

y^(3/4 - 1/3) = y^(9/12 - 4/12)

y^5/12