MENULaws of Exponents Worksheet
Simplify each expression with the laws of exponents and write the missing numbers in the boxes. A mark next to the boxes shows if your answer is right. Reload the page for 10 new expressions.
${a^m \cdot a^n = a^{m+n}}$
${\dfrac{a^m}{a^n} = a^{m-n}}$
${(a^m)^n = a^{m \cdot n}}$
${(a^m b^n)^p = a^{mp} b^{np}}$
${\left(\dfrac{a^m}{b^n}\right)^p = \dfrac{a^{mp}}{b^{np}}}$
${a^0 = 1}$
How to use the laws of exponents
Use one law at a time. A letter with no exponent has exponent 1, for example ${b = b^1}$.
Example: a³ · a⁵
The bases are the same, so add the exponents: ${a^3 \cdot a^5 = a^{3+5} = a^8}$.
Example: (4a⁴)² / (2a)³
- Raise each factor in the brackets to the power: ${(4a^4)^2} = {4^2 \cdot (a^4)^2} = {16a^{4 \cdot 2}} = {16a^8}$ and ${(2a)^3} = {2^3 \cdot a^3} = {8a^3}$.
- Divide the numbers and subtract the exponents: ${\dfrac{16a^8}{8a^3}} = {\dfrac{16}{8} \cdot a^{8-3}} = {2a^5}$.
Any power with exponent 0 is 1, so ${(5a^2bc^4)^0 = 1}$ (when ${a, b, c \ne 0}$).
The laws with proofs: Laws of Exponents.
Exponents and Radicals