Question

Simplify ((4)^-1-(5)-1)^2 * (5/8)^-1

Answer 1

Answer:

1/250

Step-by-step explanation:

$( {4}^{ - 1} - {5}^{ - 1} ) {}^{2} \times ( \frac{5}{8} ) {}^{ - 1} \\ \\ = ( \frac{1}{4} - \frac{1}{5} ) {}^{2} \times \frac{8}{5} \\ \\ = ( \frac{5 - 4}{20}) {}^{2} \times \frac{8}{5} \\ \\ = ( \frac{1}{20} ) {}^{2} \times \frac{8}{5} \\ \\ = \frac{1}{400} \times \frac{8}{5} \\ \\ = \frac{1}{50} \times \frac{1}{5} \\ \\ = \frac{1}{250}$

Simplification is simply done while following the most basic rule of mathematics that is the sequence in which the terms must be simplified.

This is given by BODMAS.

B - Brackets

O - Of

D - Division

M - Multiplication

A - Addition

S - Subtraction

Answer 2

Step-by-step explanation:

[(1/4-1/5]^2×8/5

[(5-4)/20]^2×8/5

=(1/20)^2×8/5

1/400 ×8/5

=1/50×1/5=1/250