Exponents Formula

In the expression

\(\begin{array}{l}a^{2}\end{array} \)
, a is known as base and 2 is known as the exponent. An exponent represents the number of times the base to be multiplied. For example, in
\(\begin{array}{l}a^{2}\end{array} \)
, a will be multiplied twice, i.e., a 
\(\begin{array}{l}\times\end{array} \)
a and similarly,
\(\begin{array}{l}a^{3}\end{array} \)
= a
\(\begin{array}{l}\times\end{array} \)
\(\begin{array}{l}\times\end{array} \)
a.

Here you will learn about various formulas of exponents.

The Exponents Formulas are

\(\begin{array}{l}\large a^{0}=1\end{array} \)

\(\begin{array}{l}\large a^{1}=a\end{array} \)

\(\begin{array}{l}\large \sqrt{a}=a^{\frac{1}{2}}\end{array} \)

\(\begin{array}{l}\large \sqrt[n]{a}=a^{\frac{1}{n}}\end{array} \)

\(\begin{array}{l}\large a^{-n}=\frac{1}{a^{n}}\end{array} \)

\(\begin{array}{l}\large a^{n}=\frac{1}{a^{-n}}\end{array} \)

\(\begin{array}{l}\large a^{m}a^{n}=a^{m+n}\end{array} \)

\(\begin{array}{l}\large \frac{a^{m}}{a^{n}}=a^{m-n}\end{array} \)

\(\begin{array}{l}\large (a^{m})^{p}=a^{mp}\end{array} \)

\(\begin{array}{l}\large (a^{m}c^{n})^{p}=a^{mp}c^{np}\end{array} \)

\(\begin{array}{l}\large \left ( \frac{a^{m}}{c^{n}} \right )^{p}=\frac{a^{mp}}{c^{np}}\end{array} \)

 

Solved Examples

Question 1: Solve:

\(\begin{array}{l}\frac{1}{4^{-3}}\end{array} \)

Solution: As per the The Negative Exponent Rule –

\(\begin{array}{l}\frac{1}{a^{-n}}=a^{n}\end{array} \)

\(\begin{array}{l}\frac{1}{4^{-3}} = 4^{3} = 64\end{array} \)

Question 2: Solve:

\(\begin{array}{l}\large\frac{3a^{-3}b^{5}}{4a^{4}b^{-3}}\end{array} \)

Solution:

\(\begin{array}{l}\large\frac{3a^{-3}b^{5}}{4a^{4}b^{-3}}\end{array} \)

=

\(\begin{array}{l}\large\frac{3b^{3}b^{5}}{4a^{4}a^{3}}\end{array} \)

=

\(\begin{array}{l}\large\frac{3b^{8}}{4a^{7}}\end{array} \)

1 Comment

  1. What is the formula for law of exponents

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