# Today's lesson: Myltiplying negative exponents

To understand multiplication of numbers having negative exponents , the following need to be keep under consideration to avoid any confusion

1. In both division and multiplication of powers with same base , coefficients of power are first divided or multiplied respectively

2. When powers with same base are multiplied , their exponents are added

3. When powers with same base are divided , their exponents are subtracted

## How to multiply negative exponents?

1. Move all the powers with same base in one position followed by placing multiplication signs among the powers

2. Multiply their respective coefficients

3. Add the exponents

4. Simplify the resultant power

All the four can be understood by the following equation

**Examples**

The following examples will clearly demonstrate **multiplying negative exponents** in different situations

**Solution**

The period “.” Indicate both the powers are being multiplied. So , the above expression can be written as

As in both terms 2x^{2} and 3x^{-2 } , the base is x , so using Rule 1 we will multiply their coefficients as

As both the powers are being multiplied, so exponents will be added as

Answer is 6

**Solution
**By simplifying the coefficients of product of powers , we have

By rearranging the powers with similar base , we have

So , x^{-7}y^{3 } is the answer

**Solution**

The square root of any number is equal to the number raised to half

Similarly , for cubic root , we have

By writing the square roots in its exponential forms, we have

By rearranging the powers , we have the following

Summing up all the exponents of powers , we have

So , 1 is the answer

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