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

how to multiply negative exponents

Examples


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

Solution


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

As in both terms 2x2 and 3x-2 , the base is x , so using Rule 1 we will multiply their coefficients as
examples of  multiplying negative exponents

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

multiplying exponents 

Answer is 6
solution for multiplying exponents

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

simplifying the coefficients of product of powers

By rearranging the powers with similar base , we have
rearranging the powers with similar base

So , x-7y3 is the answer
answer for multiplying negative exponents

Solution

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

square root number

Similarly , for cubic root , we have
cubic root

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

By rearranging the powers , we have the following
rearranging the powers

Summing up all the exponents of powers , we have
exponents of powers

So , 1 is the answer 


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