Jamie has 100 milliliters of a 50% isopropyl alcohol solution. How many milliliters of a 92% isopropyl alcohol solution does she need to add to this in order to obtain a 75% isopropyl alcohol solution?

9514 1404 393

Step-by-step explanation:

When a value is moved from outside the radical to inside, it gets an exponent equal to the index of the radical.

A) x³√x = √(x^(2·3+1)) = √(x^7) . . . . c = 7

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B) x∛(x²) = ∛(x^(3·1+2)) = ∛(x^5) . . . . d = 5

Alternate solution

You could use the fractional exponent equivalent of the radical and write the sum of exponents equation.

A) c/2 = 3+1/2   ⇒   c = 7 . . . . . exponents for x

B) d/3 = 1+2/3   ⇒   d = 5 . . . . . exponents for x

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The exponent rules being used here are ...

  √x = x^(1/2)

  ∛x = x^(1/3)

  (x^a)(x^b) = x^(a+b)

  (x^a)^b = x^(ab)