Simplify $2a^2{b}^{-1}\cdot 3a^{-1}{b}^3$.

Which statement correctly explains why you cannot apply the product rule to simplify $2^3\times 3^3$ by adding exponents?

What is the numerical value of ${10}^0$?

Simplify $\frac{3^5}{3^2}$.

Simplify $\frac{8^5}{2^{12}}$.

A student simplifies y⁵ / y⁷ as y² and claims this follows the quotient rule. What is the best correction and explanation?

Which exponent expression correctly represents the product $x\cdot x\cdot x\cdot y\cdot y$?

Use the power-of-a-power rule to simplify ${\left(t^3\right)}^4$.

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

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

A student says that $(6z^4{)}^0=0$ because the exponent is zero. How should this claim be judged for $z\ne 0$?

Simplify $(4a^{-2}{)}^2\cdot (3a^5)$.