Question

what are the laws of exponent?

Answer 1

a^n = a × a × ... × a

a^n · a^m = a^n+m

a^n · b^n = (a · b)^n

a^n / a^m = a^n-m

a^n / b^n = (a / b)^n

(b^n)^m = b^n·m

b^n^m = b(^n^m)

b^0 = 1

Answer 2

❒ Question -:

What are the laws of exponents ?

❒ Explanation -:

An exponent refers to the number of times a number is multiplied by itself.

Example : 5 raised to the power 3. This can be written as 5³.

This means that

5 × 5 × 5 = 125

Laws of exponent :

x is any rational number and m and n is any positive integers.

$\small\rm{1) \: {x}^{m } \times {x}^{n} = {x}^{m + n} }$

$\small\bf{ Example : \: } \rm{ 2⁵ × 2⁷ = {2}^{5 + 7} = {2}^{12} }$

$\small\rm{2) \: \dfrac{ {x}^{m} }{ {x}^{n} } = {x}^{m - n }\: \: \: \: \: \: \sf{if \: m \: >n}}$

$\small\bf{Example : \sf{ \dfrac{2⁵ }{2²} = {2}^{5 - 2} = {2}^{3} = 8 } }$

$\small\rm { 3) \: \dfrac{ {x}^{m} }{ {x}^{n} } = \dfrac{1}{ {x}^{n - m} } \: \: \: \: \: \sf{if \: n>m} }$

$\small\bf{Example : \sf{\dfrac{2³ }{2⁵} = \dfrac{1}{ {2}^{5 - 3} } } = \dfrac{1}{ {2}^{2} } = \dfrac{1}{4} }$

$\small\rm{4) \: {x}^{0} = 1}$

$\small\bf{Example : \sf{2⁰ = 1}}$