Question

$\huge{\mathfrak{Question :-}}\\\\\sf {Formulas\ of \ Exponents}$

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Answer 1

Exponents

For any real number ' a ' and any positive integer n we define $\sf\:a{}^{n}$ as :

$\tt\:a{}^{n}=a\times\:a\times\:a\:(n\:Factors)$

Here ,

• $\sf\:a{}^{n}$ is called the nth power of a.
• The real number a is called the base and n is called the exponent of the nth power of a .

Laws of Exponents :

If a ,b are positive real numbers and m,n are rational numbers ,then .

$\sf\:1)a{}^{m}\times\:a{}^{n}=a{}^{m+n}$

$\sf\:2)\dfrac{a{}^{m}}{a{}^{n}}=a{}^{m-n}$

$\sf\:3){a}^{m{}^{n}}=a{}^{mn}$

$\sf\:4)a{}^{-n}=\dfrac{1}{a{}^{n}}$

$\sf\:5){ab}^{m}=a{}^{n}\times\:a{}^{n}$

$\sf\:6)(\frac{a}{b}){}^{n}=\frac{a{}^{n}}{b{}^{n}}$

$\sf\:7)a{}^{\frac{m}{n}}=(\sqrt[n]{a} ){}^{m}$

$\rule{200}2$

More About this topic :

• Principal nth root of a negative real number

if a is a negative real number and n is an odd positive integer .Then ,the principal nth root of a is minus the principal and root of |a|.

Example : $\sf\:{-8}^{\frac{1}{3}}=-2$