aⁿxaᵐ=aⁿ+ᵐaⁿ/aᵐ=aⁿ-ᵐaⁿxbⁿ=(axb)ⁿ(aⁿ)ᵐ=aⁿᵐ

Laws of Exponents

Bases – multiplying the like ones – add the exponents and keep base same. (Multiplication Law)

Bases – raise it with power to another – multiply the exponents and keep base same.

Bases – dividing the like ones – ‘Numerator Exponent – Denominator Exponent’ and keep base same. (Division Law)

Let ‘a’ is any number and ‘m’ , ‘n’ are positive integers, then

Multiplication Law

am× an = am+n

Division Law

am÷an = am/ an = am-n

Negative exponent

a-m= 1/am

Exponent Rules

i) a0= 1

ii) (am)n= a(mn)

iii) am× bm=(ab)m

iv) am/bm= (a/b)m

Laws of Exponents-

(i)am/an= am-n

(ii)a(m)n= amn

(iii)am× bm= (ab)m

(iv)am/bm= (a/b)m

(v)a0= 1

(vi) m√(bn) =bn/m

(vii) b1/n=n√b

(viii) b-n= 1 /bn

Laws of Exponents. When multiplying like bases, keep the base the same and add theexponents. When raising a base with a power to another power, keep the base the same and multiply theexponents. When dividing like bases, keep the base the same and subtract the denominatorexponentfrom the numeratorexponent. Accordingto the product law of exponents when multiplying two numbers that have the same basethen we can add the exponents

am× an=am+n

where a, m and n all are natural numbers. Here the base shouldbe the same in both the quantities. For example,

2³× 24= 27

22/3× 21/5= 22/3 + 1/5 = 2(10+3)/15. We get, = 212/15

(-6)3x (-6)2= (-6)3+2= (-6)5