Use laws of indices (#5)

Simplify $\dfrac{(2x^2y^3)^4 \times 3x^{-3}y}{6x^5y^{10}}$, leaving your answer with positive indices.

Simplify $\dfrac{(3x^2 y^{-1})^2 \times (2x^{-1} y^3)^3}{6x^4 y^{-2}}$, giving your answer with positive indices.

Simplify $\left(\dfrac{2x^{-2}y^{3}}{4x^{3}y^{-1}}\right)^{-2}$, giving your answer using positive indices only.

Simplify $\dfrac{(2x^2 y^{-1})^3}{(4x^{-1} y^2)^2}$, giving your answer with positive indices.

Simplify $\dfrac{9^{n+2} \times 3^{n}}{27^{n+1}}$, giving your answer as an integer.

Simplify $\dfrac{(2x^3y)^2 \times 3x^4y^5}{6x^5y^6}$.

Simplify $\dfrac{(4a^3b^{-1})^2 \times 2a^{-5}b^4}{8a^2b^{-3}}$, leaving your answer with positive indices.

Simplify $(2a^{-2}b^3)^{-2} \times (4a^3b^{-1})^2$, leaving your answer with positive indices.

Simplify $\dfrac{2^{n+3} \times 4^{n}}{8^{n-1}}$, leaving your answer as a power of 2.

Simplify fully, leaving your answer in index form:

Simplify $\dfrac{(3a^2b)^2 \times 2a^4b^3}{6a^5b^2}$.

Simplify $\dfrac{(2x^3)^2 \times x^5}{4x^2}$ using the laws of indices.

Simplify $\left(\dfrac{2x^{-2}y^3}{4x^3y^{-1}}\right)^{-2}$, leaving your answer with positive indices only.

Simplify $\dfrac{4^{x+1} \times 8^{x-1}}{2^{3x}}$, giving your answer as a power of 2.

Simplify $\dfrac{(2x^2 y^{-1})^3 \times (x^{-1} y^2)^2}{4x^3 y^{-4}}$, leaving your answer with positive indices only.

Simplify $\dfrac{(3x^{-2}y^3)^2}{9x^{-5}y^4}$, leaving your answer with positive indices only.

Simplify $\dfrac{(2x^3)^4 \times 3x^2}{6x^7}$, giving your answer in its simplest form.

Simplify fully, leaving your answer in index form: