Exponents And Powers

The distance between the Sun and the Earth is 149,600,000 kilometers. The mass of the Sun is 1,989,000,000,000,000,000,000,000,000,000 kilograms. The age of the Earth is 4,550,000,000 years. The size of a hydrogen atom is 0.00000000000106 meters. These numbers are way too large or small to memorize in this way.  With the help of exponents and powers these huge numbers can be reduced to a very compact form and can be easily expressed in powers of 10.

Exponents are the repeated multiplication of any number. The number 1,000,000 can be written as

1,000,000 = 10 × 10 × 10 × 10 × 10 × 10 = 106

Thus, when 10 is multiplied 6 times we get 1,000,000. It can be expressed using power as 106. 10 is the base and 6 is the exponent. It is read as ’10 raised to the power of 6’.

The exponent is a simple but powerful tool. It tells us how many times a number should be multiplied by itself to get the desired result. Thus any number ‘a’ raised to power ‘n’ can be expressed as:

Exponents And Powers

‘a’ is the base and ‘n’ is the exponent. ‘a’ is multiplied ‘n’ times thereby exponentiation is the shorthand method of repeated multiplication.

Now, coming back to the examples we began with, we can express the distance between the Sun and the Earth with the help of exponents and powers as following:

Distance between the Sun and the Earth 149,600,000 = 1.496× 10 × 10 × 10 × 10 × 10× 10 × 10 = 1.496× 108 kilometers.

Mass of the Sun: 1,989,000,000,000,000,000,000,000,000,000 kilograms = 1.989 × 1030 kilograms.

Age of the Earth:  4,550,000,000 years = 4. 55× 109 years

Size of a hydrogen atom: 0.00000000000106 meters = 1.06 × 10-12 meters.

Solve the model solutions to the chapter Exponents and Powers that are provided in detail through simple step-step solutions to all questions in an NCERT textbooks only at Byju’s.

Practise This Question

Find the value of (32)2.