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Laws of Exponents

The laws of exponents are the laws of indices. Laws of exponents are useful to simplify algebraic expressions and solve equations. Exponent is a number raised to another number, it is represented as, bm.

Laws of exponent are as follows:

  •  b1 = b

  • b0 = 1

  • Negative exponent

            b - m = $\frac{1}{b^m}$

  • Multiplication law of exponent

           bm . bn =  (b) m + n

  • Division law of exponent

          $\frac{b^m}{b^n}$ = bm - n   

  • Power of power law of exponent

         (bm) =  bmn

         (ab)m  =  am $\times$ b m

         $(\frac{a}{b})^m$ = $\frac{a^m}{b^m}$

  • Fractional law of exponent 

    $b^{\frac{m}{n}}$ = $(b^m)^{\frac{1}{n}}$ = $\sqrt[n]{b^m}$

Related Calculators
Calculating Exponents Fractional Exponents Calculator
Adding Exponents Calculator Dividing Exponents Calculator

Laws of Exponents Examples

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Lets solve some examples by using laws of exponents.

Solved Examples

Question 1: Simplify $\frac{(x^2)^5}{x^3 \times y^2}$
Given, $\frac{(x^2)^5}{x^3 \times y^2}$

$\frac{(x^2)^5}{x^3 \times y^2}$ = $\frac{x^{10}}{x^3 \times y^2}$ (Using law (bm) =  bmn )

= $\frac{x^{10 - 3}}{y^2}$  ( Using division law of exponent )

= $\frac{x^7}{y^2}$

=> $\frac{(x^2)^5}{x^3 \times y^2}$ = $\frac{x^7}{y^2}$


Question 2: Solve $\frac{m^3 \times 27}{3m^2}$, using exponents laws.
$\frac{m^3 \times 27}{3m^2}$ = $\frac{m^3 \times 3^3}{3m^2}$

= $m^{3-2} \times 3^{3-1}$

= $m^1 \times 3^2$

= 9m

=> $\frac{m^3 \times 27}{3m^2}$ = 9m

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