# Power of 10: Positive Exponent

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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

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