Exponents and Powers for class 8

 Exponents and Powers for class 8

When a number x is multiplied several times, say n times, then the product x*x*x*x*.....n times can be written as xn  read as x raised to the power n or x to the power n.

The number x is called the base and n is called the exponent.

LAWS OF EXPONENT :

 

Exercise :

1. Simplify :

i) a⁶ × a⁸     

 = a⁶⁺⁸

 = a¹⁴ 

ii) x⁵ × x^-3

   = x^5+(-3) 

  = x^5-3 = x²

iii) z⁹ × z³× z^-6

   = z^9+3-6 

   = z⁶

iv) a²b³ × a⁵b² 

   = a²⁺⁵ × b³⁺²

   = a⁷ × b⁵

v) 5x⁷ × 3x⁴

  = 15x⁷⁺⁴ 

  = 15x¹¹ 

vi) p³q⁴ × p⁵q^-5

  =  p³⁺⁵ × q^4-5

  =  p⁸ × q^-1 

  =  p^8/q¹ 

vii) x⁷y^-5 × x^-5y³

   = x^7-5 × y^-5+3

   = x²y^-2

   = x^2/y²

viii) x^-2y⁵ × x⁰y^-7

       =  x^-2+0y^5-7 

      =  x^-2y^-2

      =  1/x²y²  

2. Simplyfy :

1. x12/x7 = x12-7 = x5 

2. z6/z-3 = z6-(-3)= z6+3 = z9 

3. m⁵n³ /m²n^-4 = m^5-2n^3-(-4) = m³n⁷ 

4. 18x9  ÷ 6x7= 18/6 x9-7 = 3x2 

5. 7a12  ÷ 56a15 = 7/56 a12-15 = 1/8*a-3= 1/8a3

6. a13b⁷ ÷ a5 b^-3 = a^13-5b^7-(-3) = a⁸b¹⁰

7. 7x14  ÷ 21x-10 = 7/21 x14-(10) =  x24/3

8. p11  ÷ p11 = p^11-11 = p⁰ = 1