IB Mathematics Analysis and Approaches Question Type 9: Summarizing Laws of Exponents Exercises

Solve for $x$: $2^x\cdot 4^{x-2}=32$ [3 marks]

Simplify $\frac{5^0+5^1}{5^2}$

Simplify $\frac{3^4\cdot 3^{-2}}{3^1}$

Expand and simplify $(x^2{y}^{-1}{)}^{-2}\times x^3$

Simplify $\frac{16^{x+1}}{8^x}$ and express the result as a power of 2

Simplify ${\left(\frac{2^5}{2^3}\right)}^2$

Simplify ${\left(\frac{a^3{b}^{-2}}{a^{-1}{b}^4}\right)}^2$

Solve for $x$: $4^{2x-1}=8^{x+2}$

Solve for $x$: $(\frac{1}{3}{)}^x=9^{x+1}$

Simplify $(-2{)}^3\cdot 4^{-2}$

Solve for $x$: $5^{2x-3}=125^{x+\frac{1}{2}}$

Simplify $9^{\frac{3}{2}}\cdot 27^{-\frac{1}{3}}$