Question

Please answer Questions 12-18! Please show work and explanations because I was absent in class and I have NO IDEA how to do this! If you are right, I will award you 60 points!! PLS HELP!!

Answer 1

12) v=0

13) w=9

14) y=5

15) z=-8

16) n=2, m=-2

17) x=3

18) 1, because . Therefore

Explanation:

12) Exponent Zero rule. Anything raise to 0 power equals 1.

13) Exponent Negative rule:

14) Exponent Quotient rule:

In this case,

15) Exponent Product rule:

In this case,

16) Same rule as #15,

17)We can work backwards here, we know and , so we need .

To achieve this, use Exponent Quotient rule, what x-4=1? x=5.

Similar base: . Put back for

18) 1*1*1*1=1. Anything raise to 0 power equals 1 (Exponent Zero rule). To prove this, any number(except 0) divided by itself equals 1.

Ex: 1/1=1, 4/4=1, .

We can prove this with the Exponent Quotient rule. . No matter how I write it, it's equal to 1.

Answer 2

12) v=0

13) w=9

14) y=5

15) z=-8

16) n=2, m=-2

17) x=3

18) 1, because
`2^(4)/{2^(4) =1`. Therefore
`2^(4)/{2^(4) = 2^(4-4)=2^(0)=1`

Explanation:

12) Exponent Zero rule. Anything raise to 0 power equals 1.

13) Exponent Negative rule:
`b^(-n) =(1)/(b^n)`

14) Exponent Quotient rule:
`(a^n/a^m)=a^(n-m)`

In this case,
`(3^3/3^5)=3^(3-5)=3^(-2)=1/3^2=1/9`

15) Exponent Product rule:
`(a^n*a^m)=a^(n+m)`

In this case,
`(5^8*5^(-8))=5^(8-8)=5^0=1`

16) Same rule as #15,
`(7^2*7^(-2))=7^(2-2)=7^0=1`

17)We can work backwards here, we know
`2^(2) = 4` and
`3^(1) =3`, so we need
`2^2/3^1=4/3`.

To achieve this, use Exponent Quotient rule, what x-4=1? x=5.

Similar base:
`(3^5/3^4)=3^(5-4)=3^(1)=1/3`. Put
`2^(2)` back for
`(4)/(3)`

18) 1*1*1*1=1. Anything raise to 0 power equals 1 (Exponent Zero rule). To prove this, any number(except 0) divided by itself equals 1.

Ex: 1/1=1, 4/4=1,
`2^4/2^4=1`.

We can prove this with the Exponent Quotient rule.
`1=(3)/(3) =(3^1)/(3^1)=3^(1-1)=3^0=1`. No matter how I write it, it's equal to 1.

The one exception is
`0^(0)`, which is undefined, since dividing by zero is illegal.

Hope this helps. ;)