Question

Hello there. May somebody help me simplify this problem? It would be very kind.

It is about radicals etc.

Answer 1

27 / (4x⁶y⁸)

Explanation:

`(4(3x^(2)y^(4))^(3))/((2x^(3)y^(5))^(4))`

When raised to a power, multiply the exponents.

`(4(3^(3)x^(6)y^(12)))/(2^(4)x^(12)y^(20)) \\\\(2^(2)3^(3)x^(6)y^(12))/(2^(4)x^(12)y^(20))`

When dividing, subtract the exponents.

`2^(2-4)3^(3)x^(6-12)y^(12-20)\\2^(-2)3^(3)x^(-6)y^(-8)`

Move negative exponents to the denominator.

`(3^(3))/(2^(2)x^(6)y^(8))\\(27)/(4x^(6)y^(8))`