Match the numerical expressions to their simplified forms

Step-by-step explanation:

Required

Match each expression to their simplified form

1.

Simplify the expression in bracket by using the following law of indices;

The expression becomes

Split the fraction in the bracket

Simplify the fraction by using the following law of indices;

The expression becomes

Further simplify the expression in bracket by using the following law of indices;

The expression becomes

Hence,

2.

Simplify the expression in bracket by using the following law of indices;

The expression becomes

Further simplify the expression in bracket by using the following law of indices;

The expression becomes

Hence,

3.

Simplify the numerator as thus:

Simplify the denominator as thus:

Simplify the expression in bracket by using the following law of indices;

The expression becomes

Hence,

4.

Simplify the expression in bracket by using the following law of indices;

The expression becomes

Hence

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the linear relationship that represents a variation in direct proportion is the linear function that varies according to the numbers of its domain, for example the cost of producing x number of items can be represented in direct proportion by f (x) = mx + b, where m is the constant of proportionality, x the number of articles produced and b the fixed cost