91Ó°ÊÓ

${\text{a}}^{\text{x}}→$a is the base and x is exponent.

The power is the result of repeated multiplication of the same factor.

The expressionsa^xthis means that a has been used as a factor x times

Example: Find the base and the exponent of 2⁷ and evaluate the value.

Rule: ${\text{a}}^{\text{x}}→$a is called base and x is exponent.

a = 2 and x = 7

Base = 2 and exponent = 7

Evaluate: $2^7=2 · 2 · 2  · 2 · 2 · 2 · 2 =128$

Evaluate the expression 72 ÷ x² when x = – 4

According to the exponent rule:

${\text{a}}^{\text{x}}→$a is called base and x is power.

a = x and x = 2

In repeated multiplication:$x^2  =  x  ·  x$

Rule:The product of two negative integers is positive and quotient of two positive integers is positive.

When x = – 4:$\frac{72}{x^2}  =  \frac{72}{x  ·  x}  =  \frac{72}{-  4  ·  -  4}  =  \frac{72}{16}  =  \frac{9}{2}$

The value of72 ÷ x²after evaluating the power is $\frac{9}{2}$ when x = – 4.