Laws of Exponents for Real Numbers

The laws of exponents simplify the multiplication and division operations and help to solve the problems easily. In this article, we will be knowing the six important laws of exponents.

Laws of Exponents

Let $a>0$ be a real number and $p$ & $q$ be rational numbers. Then we have

• $a^{p}\times a^{q}=a^{p+q}$
• $(a^{p})^{q}=a^{pq}$
• ${\frac {a^{p}}{a^{q}}}=a^{p-q}$
• $a^{-p}={\frac {1}{a^{p}}}$
• $a^{\frac {1}{p}}={\sqrt[{p}]{a}}$
• $a^{0}=1$

Examples

1. $5^{2}\times 5^{5}=5^{2+5}=5^{7}$
2. $(5^{2})^{3}=5^{2\times 3}=5^{6}$
3. ${\frac {5^{6}}{5^{4}}}=5^{6-4}=5^{2}=25$
4. $5^{-2}={\frac {1}{5^{2}}}={\frac {1}{25}}$
5. $5^{\frac {1}{3}}={\sqrt[{3}]{5}}$
6. $5^{0}=1$