Interpret $5^3$ and determine its numerical value using the definition of exponents as repeated multiplication.

Simplify $4x^2\cdot 5x^3$.

Simplify: ${(-4)}^2\times {(-4)}^3\times z^5\times z^{-2}$

Calculate $\frac{4^3}{4}$.

Simplify $\frac{x^4\cdot x^3}{x^5}$ by applying the product and quotient rules in sequence.

Which explanation best justifies why multiplying powers with the same base will mean that you can add the exponents, while dividing them will mean that you can subtract the exponents?

Use the product rule to simplify $5^3\cdot 5^2$.

Simplify ${\left(3xy\right)}^2$ by distributing the exponent.

Simplify ${\left(2x^{2}y\right)}^3$ fully, applying the power-of-a-product and power-of-a-power rules where appropriate.

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

Which rewrite removes all negative exponents from $\frac{5a^{-2}}{b^{-3}}$?

Simplify $\left(2x^{-3}{)}^2\right(5x^4{)}^1$.