Chapter 1.2, Problem 62HP

To determine

To write: an expression having exponents, at least 3 different operations and two sets of parentheses and evaluate that expression.

Answer to Problem 62HP

  $a^2-[(b^2+c)\cdot d]$

Simplified expression $=g-f$

Explanation of Solution

Given information:

To use exponents, at least 3 different operations and two sets of parentheses to write an expression.

Concept Used:

BODMAS Rule:

B Bracket − ( ) or [ ] or { }

O Order or Power - $\sqrt{}$ or ( )²

D Division $(÷)$

M Multiplication $(\times )$

A Addition $(+)$

S Subtraction $(-)$

Calculation:

Assume a, b, c and d be the four values that are combined together to form an expression having exponents, at least three different operations and two sets of parentheses.

The expression having all the required elements is expressed as:

  $a^2-[(b^2+c)\cdot d]$

Squaring the term bwithin round brackets ( ) (Q BODMAS Rule)

  $a^2-[(p+c)\cdot d]$ (Assume $b^2=p$ )

Solving the term having round brackets ( ) within the square brackets [ ] (Q BODMAS Rule)

  $a^2-[e\cdot d]$

Solving the term within square brackets [ ] (Q BODMAS Rule)

  $a^2-f$ (Assume $p+c=e$ )

Squaring the term a before subtracting by f (Q BODMAS Rule)

  $=g-f$ (Assume $a^2=g$ )

The expression having exponents, at least three different operations and two sets of parentheses: $a^2-[(b^2+c)\cdot d]$ .

The evaluation of the expression

  $a^2-[(b^2+c)\cdot d]$ comes out to be $g-f$ .