What I learned this week

This week, I learned about the exponents laws, and here are some of them:

Rule: When multiplying powers with the same base, you add the exponents.

1) 5^35^4 = 5^7

5•5•5•5•5•5•5= 5^7

2) 3^33^2 = 3^5

3•3•3•3•3= 3^5

 

Rule: When dividing powers with the same base, you subtract the exponents.

1) 5^5 ÷ 5^3 = 5^2

2) 5^7 ÷ 5^4 = 5^3

 

Rule: To raise a power to a power, multiply the exponents.

21db7b010479c5e122a4126e5c60ad41

 

Rule: When a product is raised to an exponent, you can rewrite each factor in the product with the same exponent.

( 3 × 2 ) ^3

( 3 × 2 ) ( 3 × 2 ) ( 3 × 2 ) = 3^22^3

Rule: When a quotient is raised to an exponent, you can rewrite each number in the quotient with the same exponent.

1) 5^4 ÷ 5^4 = 5^0 = 1

Rule: When the exponent of a power is zero, the value of the power is 1 (as long as the base is zero)

[ 2× ( -3 ) ] ^5

= 2^5(-3)^5

= -7776

 

Word problems with fractions.

I earned $250 at my job. I used 1/10 at McDonald’s, 1/4 for shoes and 1/8 for clothing. How much money do I have left for savings?

1. First I add all the money that I used.

1/10 + 1/4 + 1/8 =  19/40

2. Now multiply 250/1 × 19/40 (total of money that I used)

250/1 × 19/40 = 118 3/4  or 475/4

3. Transform the fraction into a decimal by dividing the numerator and the denominator.

475/4 ~  475 ÷ 4 = 118.75

4. I used $118.75 of $250.

5. 250 – 118.75 = 131.25

6.I have $131.25 for savings.