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Exponents Formula

In the expression, $a^{2}$, 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 $a^{2}$, a will be multiplied twice, i.e., a $\times$ a and silimarlt $a^{3}$ = a $\times$ a $\times$ a.

Here we will learn about various formulas of exponents

The Exponents Formulas are

$\large a^{0}=1$

$\large a^{1}=a$

$\large \sqrt{a}=a^{\frac{1}{2}}$

$\large \sqrt[n]{a}=a^{\frac{1}{n}}$

$\large a^{-n}=\frac{1}{a^{n}}$

$\large a^{n}=\frac{1}{a^{-n}}$

$\large a^{m}a^{n}=a^{m+n}$

$\large \frac{a^{m}}{a^{n}}=a^{m-n}$

$\large (a^{m})^{p}=a^{mp}$

$\large (a^{m}c^{n})^{p}=a^{mp}c^{np}$

$\large \left ( \frac{a^{m}}{c^{n}} \right )^{p}=\frac{a^{mp}}{c^{np}}$

 

Solved Examples

Question 1: Solve $\frac{1}{4^{-3}}$

Solution: As per the The Negative Exponent Rule –

$\frac{1}{a^{-n}}=a^{n}$

$\frac{1}{4^{-3}} = 4^{3} = 64$

Question 2: Solve $\large\frac{3a^{-3}b^{5}}{4a^{4}b^{-3}}$

= $\large\frac{3b^{3}b^{5}}{4a^{4}a^{3}}$

= $\large\frac{3b^{8}}{4a^{7}}$

More topics in Exponential Formula
Square Root Formula Sum of Squares Formula
Difference of Squares Formula Cube Formula
Cube Root Formula Binomial Expansion Formula
Exponential Function Formula Exponential Equation Formula
Double Time Formula
Related Formulas
Fibonacci FormulaFrustum of a Right Circular Cone Formula
Fourier Series FormulaHalf Angle formula
Geometric Series FormulaImplicit Differentiation Formula
Inverse Hyperbolic Functions FormulaLinear Regression Formula