# Power of 10: Negative Exponent

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

**Rules to find the negative exponent of 10**

Suppose we have an expression having 10^{-n}.

In normal course the value of 10

^{-n}is found by multiplying the base

10 'n' times in the denominator and putting a 1 in the numerator.We use a shortcut to solve such problem. We look at the exponent and then write a decimal point followed by as many zeros as one less than exponent and a 1.

Evaluate 10^{-3}

### Solution

**Step 1:**

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

The base is 10 and the exponent is −3.

**Step 2:**

In normal course the value of 10^{-3} can be found by multiplying the base 10 three times in the denominator and putting a 1 in the numerator.

10^{-3} = = 0.001

**Step 3:**

Using a shortcut, we find that the exponent is -3. We write a decimal point followed by two (1 less than 3) zeros and a 1.

So 10^{-3} = 0.001

Evaluate 10^{-5}

### Solution

**Step 1:**

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

The base is 10 and the exponent is −5.

**Step 2:**

In normal course the value of 10^{-5} is found by multiplying the base 10 five times in the denominator and putting a 1 in the numerator.

10^{-5} = = 0.00001

**Step 3:**

Using a shortcut, we find the exponent is -5. We write a decimal point followed by four (1 less than 5)zeros and a 1.

So 10^{-5} = 0.00001