Negative Exponents

Suppose we have number like

Here,

  Exponent(Power) is negative

 

It means

  10 ^{− 2} = 1/10 ²

= 1/100

= 001/100

= 0.01

∴ 10 ⁻² = 0.01

 

  10 ^{− 4} = 1/10 ⁴

 = 1/10000

 = 00001/10000

= 0.0001

 

  2 ^{− 4} = 1/2 ⁴

         = 1/(2 × 2 × 2 × 2)

         = 1/(4 × 4)

         = 1/16

 

  3 ^{− 2} = 1/3 ²

= 1/(3 × 3)

= 1/9

 

  6 ^{− 3} = 1/6 ³

 = 1/(6 × 6 × 6)

 = 1/(36 × 6)

 = 1/216

 

  (1/3) ^-2 = 1 ^-2 /3 ^-2

  = 1/3 ^-2

  = 3 ²

  = 9

 

(1/ 10) ^{- 4} = 1 ^-4 /10 ^-4

   = 1/10 ^-4

   = 10 ⁴

   = 10000

 

  ( 2 / 3) ^{- 3} = 2 ^-3 /3 ^-3

   = ((1/2 ³ ))/((1/3 ³ ) )

   = 1/2 ³  ÷ 1/3 ³

   = 1/2 ³  × 3 ³ /1

   = 3 ³ /2 ³

   = (3 × 3 × 3)/(2 × 2 × 2)

  = (9 × 3)/(4 × 2)

  = 27/8