Indices

Example :-

1.   Find the values of the unknown in the following equation

a)   10k = 0.01

b)   (1/5^)h = 1

Answer:-

a) 10^k = 0.01

10^k = 1/100

10^k = 1/10^-2

10^k = 10^-2

K = -2

b) (1/5) ^h = 1

(1/5) ^{h =} (1/5) ⁰

H = 0

2.   Use the laws & properties of indices to simplify the given expressions:-

a)   2h^-2 x 4h⁵

b)   RT⁹ ÷ R^-1_T³

Answer:-

a)   2h^-2 x 4h⁵

= 8h-2+5

= 8h³

b)   RT⁹ ÷ R^-1_T³

= R^{1 - - 9} T^9-3

=R²T⁶

3.   Solve the following of indices, evaluate:-

a) 3^x = 27

b) 81 = 9^2x+3

Answer:-

a) 3^x = 27

3^x = 3³

X = 3

   

b) 81 = 9^2x+3

9² = 9^2x+3

2 = 2x + 3

2-3 = 2x

-1 = 2x

-½ = x