9514 1404 393
Answer:
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
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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)