# CLASS-7IMPORTANT RULES OF EXPONENTS

IMPORTANT RULES OF EXPONENTS

1)  In, a⁶ = a X a X a X a X a X a, we should read as ‘a’ to the power 6 (Six), base = a , index = 6 .

2)  in, b⁸ = b X b X b X b X b X b X b X b, we should read as ‘b’ to the power 8 (Eight), base = b, index = 8.

3)  in, y= y X y X y, we should read as ‘y’ to the power 3 (Three) or ‘y’ cubed (or cube), base = y, index = 3.

4) in, z² = z X z, we should read as ‘z’ to the power of 2 (Two) or ‘z’ square ( or squared), base = z, index = 2.

5)      z¹ = z

6)     (-1)ⁿ  = 1, when index ‘n’ is even

7)    (-1)ⁿ  = - 1, when index ‘n’ is odd

1

8)    Z  X  -------- =  1

Z

1

9)     Z  ÷ Z   =    Z   X  ---------  =  1

Z

1

10)     ----------  =  a⁻ᵐ

aᵐ

This is called the Reciprocal of a power is written as a power with an index equal to the negative of the index of the power.

11)  The laws of Multiplication –   aᵐ X aⁿ  = aᵐ⁺ⁿ, where ‘m’ & ‘n’ are numbers, and ‘a’ is a non-zero number.

1

12) The laws of division,  aᵐ ÷  aⁿ  =  aᵐ X -------- =  aᵐ⁻ⁿ,

aⁿ

where ‘m’ & ‘n’ are numbers, and ‘a’ is a non-zero number.

13)  The laws of power,  (aᵐ)ⁿ = aᵐⁿ, where ‘m’ & ‘n’ are numbers, and ‘a’ is a non-zero number.

14) where ‘a’ is non zero number but index is ‘0’ (zero), then  a⁰ = 1

15) laws of th power of a product,  ( a X b )ⁿ  = aⁿ X bⁿ

aⁿ

and,   (a / b)ⁿ  =  ----------  =   aⁿ / bⁿ

bⁿ