Question

Simplify
i) $[(4^{-1}) - (5)^{-1}]^{2}*(5/8)^{-1}$
ii) $[(2)^{-1} + (4)^{-1} + (3)^{-1}]^{-1}$

Answer 1

Answer:

When silver chloride is exposed to sunlight, photolytic decomposition reaction takes place i.e the decomposition reaction carried out by sunlight . AgCl is broken down into Ag and Cl.This is a reaction used in black and white photography.

2AgCl ----------> 2Ag   +     Cl

Silver              Silver     Chlorine

Chloride

(White)

Answer 2

Answer:

i)

Simplify each term

(1/4 - 1/5)^2 × (5/8)^-1

To write 1/4 as a fraction with a common denominator, multiply by 5/5

(1/4 × 5/5 - 1/5)^2 × (5/8)^-1

To write -1/5 as a fraction with a common denominator, multiply by 4/4

(1/4 × 5/5 - 1/5 × 4/4)^2 × (5/8)^-1

Write each expression with a common denominator of 20, by multiplying each by appropriate factor of 1

(5/20 - 4/20)^2 × (5/8)^-1

Combine the numerators over the common denominator

(5 - 4/20)^2 × (5/8)^-1

Subtract 4 from 5

(1/20)^2 × (5/8)^-1

Apply product rule to 1/20

1^2/20^2 × (5/8)^-1

One to any power is one

1/20^2 × (5/8)^-1

Raise 20 to the power of 2

1/400 × (5/8)^-1

Change the sign of exponent by rewriting the base as its reciprocal

1/400 × (8/5)

Cancel the common factors of 8

1/50 × 1/5

Multiply 1/50 and 1/5

1/50 × 5

Multiply 50 by 5

1/250

The result can be shown in multiple forms:

Exact form : 1/250

Decimal form : 0.004

ii)

Simplify each term

(1/2 + 1/4 + 1/3)^-1

Find the common denominator

(6/12 + 3/12 + 4/12)^-1

Combine the numerators over the common denominator

(6 + 3 + 4/12)^-1

Simplify by adding numbers

(13/12)^-1

Change the sign of the exponent by rewriting the base as its reciprocal

12/13

The result can be shown in multiple forms:

Exact form : 12/13

Decimal form : 0.923076923076...

(if you find any error in my answer or have a doubt about the answer please comment I will try my best to help you)