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
The following examples will clearly demonstrate multiplying negative exponents in different situations
The period “.” Indicate both the powers are being multiplied. So , the above expression can be written as
As in both terms 2x2 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
By simplifying the coefficients of product of powers , we have
By rearranging the powers with similar base , we have
So , x-7y3 is the answer
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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