Practice Exponent Rules in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A set of laws governing how exponents behave under multiplication, division, and raising to a power: product rule (a^m \cdot a^n = a^{m+n}), quotient rule (a^m / a^n = a^{m-n}), power rule ((a^m)^n = a^{mn}), zero exponent (a^0 = 1 for a \neq 0), and negative exponent (a^{-n} = \frac{1}{a^n}).
Since a^3 = a \cdot a \cdot a and a^2 = a \cdot a, multiplying them gives a \cdot a \cdot a \cdot a \cdot a = a^5. You just add the counts. All the other rules follow the same logic of counting how many times you multiply.
Example 1
easySimplify \frac{x^5 \cdot x^3}{x^2}.
Example 2
mediumSimplify (2x^3y)^4.
Example 3
mediumSimplify \frac{(3a^2)^3}{9a^4}.
Example 4
mediumSimplify \frac{(2m^3)^2}{4m}.