Introduction to Exponents and Powers

Chapter thirteen Exponents and Powers

Introduction to Exponents and Powers

Exponents and powers help in writing the large numbers in a shorter form which we can read, understand and compare easily. A number placed in a superscript position to the right of another number or variable indicates repeated multiplication.

The short notation ten to the fourth power stands for the product ten multiplied by ten multiplied by ten multiplied by ten. Here 'ten' is called the base and 'four' the exponent. The number ten to the fourth power is read as ten raised to the power of four or simply as the fourth power of ten. Ten to the fourth power is called the exponential form of ten thousand.

a raised to the power b. Exponent

Base +

a raised to the power b

For example: a squared indicates a multiplied by a. a cubed indicates a multiplied by a multiplied by a. In expression twenty-five, two is called the base and five is called the exponent or power. Two to the fifth power equals two multiplied by two multiplied by two multiplied by two multiplied by two equals twenty-five.

i) Express two hundred fifty-six as a power of two.

Two multiplied by two multiplied by two multiplied by two multiplied by two multiplied by two equals two to the eighth power equals two hundred fifty-six.

ii) Which one is greater sixty-two or two to the sixth power?

Sixty-two equals six multiplied by six equals thirty-six. Two to the sixth power equals two multiplied by two multiplied by two multiplied by two multiplied by two multiplied by two equals sixty-four. So, two to the sixth power is greater than sixty-two.

Laws of exponents

Laws of Exponents