# Power of 10: Positive Exponent

In this lesson, we deal with problems involving expressions with 10 as base having positive exponents.

Rules to find the positive exponent of 10

Suppose we have an expression having 10n.

• In normal course the value of 10n is found by multiplying the base
10 'n' times.

• We also use a shortcut to solve such problem. We look at the exponent and then write a 1 followed by as many zeros as the exponent.

Evaluate 106

### Solution

Step 1:

Here we have an expression involving power of ten with a positive exponent.

The base is 10 and the exponent is 6.

Step 2:

In normal course the value of 106 can be found by multiplying the base 10 six times.

106 = 10 × 10 × 10 × 10 × 10 × 10

Step 3:

Using a shortcut, we look at the exponent and then write a 1 followed by as many zeros as the number in the exponent. Since the exponent is a 6, we write a 1 followed by six zeros.

So 106 = 1,000,000

### Solution

Step 1:

Here we have an expression involving power of ten with a positive exponent.

The base is 10 and the exponent is 9.

Step 2:

In normal course the value of 109 can be found by multiplying the base 10 nine times.

109 = 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10

Step 3:

Using a shortcut, we look at the exponent and then write a 1 followed by as many zeros as the exponent. Since the exponent is 9, we write a 1 followed by nine zeros.

So 109 = 1,000,000,000