Daily Archives: October 30, 2016

what i learned this week – exponent laws

Posted on by under Math 9

the week of oct 24th, 2016:

The skill that we focused on the most this week is learning exponent laws

challenges and achievements:

I didn’t know any of the laws before the lessons, so the concept was new to me. I found that the laws were not very complicated and were easy to learn and follow along with. While doing the homework, I noticed that I had memorized every almost every exponent law/rule

visual: some of the exponent laws that I learned this week

rule : when multiplying powers with the same base, you add the exponents

explanation : when you are multiplying powers with the same base, you add all the exponents together to give you a sum which will be the new exponent for the one base

3^2\cdot3^4 =3^{2+4}

= 3^6

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rule : when the exponent of a power is zero, the value of the power is one (as long as the base is not zero)

explanation : when your power has an exponent of 0, the value of the equation is 1. The only time that this rule doesn’t work is when the base is zero.

4^3\div4^3

= 4^{3-3}

= 4^0=1

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rule : when a product is raised to an exponent, you can rewrite each number in the product with the same exponent 

explanation : when you have a product and it is raised to an exponent, you simply rewrite each number that the product contains with the same exponent

(3\cdot2)^2

= (3\cdot2)(3\cdot2)

= 3^2\cdot2^2

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rule : to raise a power to a power, multiply the exponents

explanation : when you have to raise a power to a power, you take the two exponents and multiply them and then you use that protect as the new exponent to your base

(2^4)^5

= (2^4)(2^4)(2^4)(2^4)(2^4)

= 2^{4+4+4+4+4}

= 2^{20}

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