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# Math Problem: Laws of Exponents (Math Problem Sample)

Instructions:

What are three laws of exponents (for multiplication, division, and powers)? Write and explain each law. Why do we use exponents in scientific notation (you can provide an example)?
Write 2 problems containing exponents for your peers to simplify. Return to the discussion to check your peers’ understanding and offer help as needed. Be sure to post the answers at the close of the module.

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Content:

Laws of Exponents
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Laws of Exponents
Repeated multiplication of the same number by itself can be very long and elaborate but the scenario can be simplified in from of shorthand. The shorthand is referred to as an exponent or a power and a perfect example is when a number like 3 is multiplied by itself four times i.e. 3x3x3x3=34. The superscript 4 is referred to as an exponent or power whereas 3 is referred to as the base. The product in this example is pronounced as "three raised to the fourth powerâ€.
The Three Laws of Exponents
Multiplication Law
Ya Yb= Ya+b
When multiplying the same number by itself, the exponents are normally added. This means that powers of the same base are added when being multiplied. An example of this is:
Y4 Y3= Y 7. In this case the base is the same i.e. Y and therefore its exponents are added to get Y7.
The Division Law
Ya /Yb = Y a-b
Exponents of the same base are subtracted from each other in case of division. In this case the base is Y and the exponents are a and b. An example of this is:
Y7 / Y4 = Y 3
The Law of Powers
1 (XY) a = X a Ya
In instances where there are two different factors under the same power, each factor is raised to the same power. In this case the two factors are X and Y under the same power a. An example of this is:
(XY) 5 = X 5 Y5
2 (Ya)b = Y ab
Exponents are multiplied in instances of a power of a power. In this case b is a power of power a and therefore the exponents will be multiplied. An example of this is:
(Y2)3 =Y6
3 Y 1/a = a â€šY
The exponent root of the base is determined in case the exponent is a denominator of 1. In this case the exponent is a and the base is Y. An example of this is
Y 1/5 = 5 â€šY. This means that the fifth root of Y should be determined.
4 Y-a = 1/Ya
In case of a negative power, the base is raised to the equivalent positive power as a denominator of 1. An example of this is:
Y-2 = 1/Y 2
5 Y0 = ...
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