91Ó°ÊÓ

Let a, b, c and d be the four values which form an expression.

An expression having exponents, at least three different operations and two sets of parentheses is,

$a^2−\left[\right(b^2+c)â‹\dots d]$

Here, a and b have exponents 2. Addition, subtraction and multiplication are the three different operations and round brackets ( ), square brackets [ ] are the two sets of parentheses.

The expression $b(c−d)−e$can be written as

$\begin{array}{l}b(c−d)÷e=\left[\right(b×c)−(b×d\left)\right]÷e\\ \text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰}=(bc−bd)÷e\\ \text{ â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰â¶Ä‰}=\frac{(bc−bd)}{e}\end{array}$

$a^2−\left[\right(b^2+c)â‹\dots d]$

Squaring the term within round brackets ( ) (QBODMAS Rule)

$a^2−\left[\right(p+c)â‹\dots d]$(Assume $b^2=p$)

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

$a^2−[eâ‹\dots d]$

Solving the term within square brackets [ ] (QBODMAS Rule)

$a^2−f$(Assume $p+c=e$)

Squaring the term a before subtracting by f (QBODMAS Rule)

$=g−f$(Assume $a^2=g$)

The expression having exponents, at least three different operations and two sets of parentheses:$a^2−\left[\right(b^2+c)â‹\dots d]$.

The evaluation of the expression$a^2−\left[\right(b^2+c)â‹\dots d]$ comes out to be $g−f$.