Express x in terms of y?

Question

If (x^3)^4=(y^2)^3

Express x in terms of y.

Please include full working with explanation.

Thanks!

Answer 1

(x³)⁴ = (y²)³

Formula : [ (a^m)ⁿ = a^mn ]

(x^3·4) = (y²·³)

Simplify

(x¹²) = (y⁶)

take 6th root each side

6th root (x¹²) = 6th root (y⁶)

Note : [ n th root A = A^1/n ]

(x¹²)^1/6 = (y⁶)^1/6

Formula : [ (a^m)ⁿ = a^mn ]

(x^12/6) = (y^6/6)

x² = y

x = √y

y = x²

check the equation: (x³)⁴ = (y²)³

Let x = 2

then y = x² = 4

(2³)⁴ = (4²)³

(8)⁴ = (16)³                       [ 2³ = 8  , 4² = 16 ]

(8)⁴ = (8·2)³

(8)⁴ = (16)³

(8)⁴ = (8)³·(2)³

(8)³(8) = (8)³·(8)

Simplify

1 = 1