Question Type 3: Applying indices and negative exponents Exercises

Simplify $(y^{-2}z^3)^2$. [2 marks]

Simplify $\displaystyle\frac{(xy^2z\cdot x^{-2}y^2z)^{-1/6}\cdot xy\cdot(z^{-2}xy)^{-1/2}}{(x^{-2}y^4)^3}$

Simplify $\left(\frac{3x^2y^{-3}}{9x^{-1}y^2}\right)^{-2}$

Simplify $x^{-3}y^4 \cdot x^2y^{-1}$, giving your answer with positive exponents.

Simplify $(x^{-1/2}y^{3/2})^2$

Simplify $\frac{x^3y^{-2}}{x^{-1}y^3}$

Simplify $(a^2b^{-1})^{-3}$, giving your answer with positive exponents.

Simplify $\frac{2^3 \cdot 2^{-5}}{2^{-1}}$

Simplify $\sqrt{\frac{x^4}{x^{-2}}}$

$\frac{(2x^{-3})^2 \cdot x^4}{2^{-1}x^{-2}}$