Question Type 9: Summarizing laws of exponents Bootcamps

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

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

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

Simplify $\bigl(\dfrac{2^5}{2^3}\bigr)^2$

Simplify $9^{\tfrac32} \cdot 27^{-\tfrac13}$

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

Simplify $\bigl(\tfrac{a^3 b^{-2}}{a^{-1} b^4}\bigr)^{2}$

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

Solve for $x$: $2^{x} \cdot 4^{x-2} = 32$

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

Solve for $x$: $5^{2x-3} = 125^{x+\tfrac12}$

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