Question

(6x^4/2xy^3)^3=

36x^12/y^9

27x^9/y^9

3x^11y^9

Answer 1

well you need to recognise that the power of 3 acts on every part.

You also need to know the index law for power of a power. Which requires you to multiply powers

\[(x^a)^b = x^{a \times b}\]

the easiest way to attempt this problem is to simplify the terms inside the brackets first

\[\frac{6x^4}{2xy^3} = \frac{3x^3}{y^3}\]

which saw a common factor of 2x removed

now apply the power of a power law

\[(\frac{3x^3}{y^3})^3=\frac{3^3 (x^3)^3}{(y^3)^3}\]

which is

\[\frac{27(x^3)^3}{(y^3)^3}\]

now just use the power of a power rule above.