IB Mathematics Analysis and Approaches Question Type 3: Applying Indices and Negative Exponents Exercises

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

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

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

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

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

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

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

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

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

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