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2 votes
Which expression is equivalent to (x^27y)^1/3?

A) x^3 (3√y)

B) x^9 (3√y)

C) x^27 (3√y)

D) x^24 (3√y)

2 Answers

5 votes
Remember that (xᵃ. yᵇ)ⁿ = xᵃⁿ.yᵇⁿ

(x²⁷.y)¹/³ = x⁽²⁷ˣ¹/³⁾. y¹/³

x⁽²⁷ˣ¹/³⁾. y¹/³ =x⁸. y¹/³ = x⁹. ∛y. NONE OF THE ANSWERS, UNLESS YOU HAVE OMITTED SOMETHING, JUST AS 27 IS THE EXPONENT OF X AND ALSO ANOTHER 27 THAT MULTIPLIES Y??, In this case, it will be b
User Dennis Doomen
by
8.2k points
7 votes

Answer:

Option B).
x^(9).(\sqrt[3]{y} ).

Explanation:

The given expression is
(x^(27)y)^{(1)/(3) }.

We have to further simplify so that we can get the answer as shown in the options.


(x^(27)y)^{(1)/(3) }=(x^(27))^{(1)/(3)}(y)^{(1)/(3)}

[ As
(x^(a).y^(b))^(m)=(x^(a))^(m).(y^(b))^(m) ]

Now (
(x^(27))^{(1)/(3)}(y)^{(1)/(3)}=(x^{(27)/(3) }).(y^{(1)/(3) } )=x^(9).(\sqrt[3]{y} )

Therefore Option B. is the answer.

User Omoman
by
8.4k points
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