MULTIPLY POWERS
Multiply powers:
In the page "Multiply powers" we are going to learn about how to multiply two or more terms involving exponents.
Basic rules of multiply powers
Rule 1:
When we have to simplify two or more the terms which are multiplying with same base,then we have to put the same base and add the powers.
Rule 2:
Whenever we have two terms which are diving with the same base,we have to put only one base and we have to subtract the powers.
Rule 3:
Whenever we have power to the power,we have to multiply both powers.
Rule 4:
Anything to the power zero is 1.
Rule 5:
If we have same power for 2 or more terms which are multiplying or dividing,we have to apply the powers for every terms.
Note:
This rule is not applicable when two are more terms which are adding and subtracting.
For example (x + y) ^m = (x^m + y^m) is not correct
How to move an exponents or powers to the other side ?
 |
If the power goes from one side of equal sign to the other side,it will flip. that is x = 4² |
What is exponent and power?
The other names of exponent are index and power.
Other things:
Point 1:
If we don't have any number in the power then we have to consider that there is 1
Negative numbers with fractions
Point 2:
Incase we have negative power for any fraction and we want to make it as positive, we can write the power as positive and we should write its reciprocal only. For example
Negative numbers with negative exponents
Find the value of (-5) ³
To find value of the above expression, first we have to consider the power.
- If the power is odd, then the answer will have negative sign.
- If the power is even, then the answer will have positive sign.
here, the power of -5 is 3, that is odd. So, the answer will have negative sign and we have to multiply the base three times.
Finally we will get -125 as the answer.
Procedure of multiplying two polynomials with exponents
We will multiply two or more polynomials in the following order.
(1) Symbol
(2) Number
(3) Variable
Let us see how it works
Multiply ( 5 x² ) and (-2 x³)
= ( 5 x² ) x (-2 x³)
= 10 x⁵
Example problems of exponent properties involving products
Question 1 :
Simplify (5x²)⁴ x (2x)³
Solution :
= (5x²)⁴ x (2x)³
5⁴ = 5 x 5 x 5 x 5
2³ = 2 x 2 x 2
Since x⁸ and x³ are having same base, we can combine these terms.
Let us see the next example on "Multiply powers"
Question 2 :
If 5 √5 x 5³= 5 ⁽ⁿ⁺²⁾ then find the value of n.
Solution :
Let us see the next example on "Multiply powers"
Question 3:
Simplify (52 x⁶/13x⁻⁷)
Solution :
= (52 x⁶/13x⁻⁷)
We have negative power for the x term which is in the denominator.To make it as positive we are going to write it in numerator.
= (52 x⁶x⁷/13)
= 4 x⁽⁶⁺⁷⁾
= 4 x¹³
Let us see the next example on "Multiply powers"
Question 4 :
Simplify (-7x²) (x⁴)
Solution :
= (-7x²) (x⁴)
= -7 x⁽²⁺⁴⁾
= -7 x⁶
Let us see the next example on "Multiply powers"
Question 5 :
Simplify (10 x y³ z²) (-2 x y⁵z)
Solution :
= (10 x y³ z²) (-2 x y⁵z)
= -20 x^(1+1) y^(3+5) z^(2+1)
= -20 x²y⁸z³
Let us see the next example on "Multiply powers"
Question 6 :
Simplify (-5 xyz) (4 y⁵z) y³
Solution :
= (-5 xyz) (4 y⁵z) y³
= -20 x y⁵y³z z
= -20 x y^(5+3) z^(1+1)
= - 20 x y⁸z²
Let us see the next example on "Multiply powers"
Question 7 :
Simplify (7 a b² c³) (¾ a b c⁴)
Solution :
= (7 a b² c³) (¾ a b c⁴)
= (21/4) a^(1+1)b^(2+1)c^(3+4)
= (21/4) a²b³c⁷
Question 8 :
Simplify (-4 a³) (-5 a⁴)
Solution :
= (-4 a³) (-5 a⁴)
= 20 a^(3+4)
= 20 a⁷
Question 9 :
Simplify (2 a³) (¼) a⁴
Solution :
= (2 a³) (¼) a⁴
= (2/4)a^(3+4)
= (1/2) a⁷
Question 10 :
Simplify (10 p³) (7/25) p⁷
Solution :
= (10 p³) (7/25) p⁷
= 10(7/25)p^(3+7)
= (1/2) a¹⁰
After having gone through the stuff given above, we hope that the students would have understood "Let us see the next example on "Multiply powers".
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