Math Problems, Show all work 10 pts!!?!!!!?

Question

16. Solve: 1/3y-1/2 Less than 5/6y+1/2
17. a. (-2x)^0=_______
b. Simplify: (-3x)^2
c. Simplify: 1/(6^-2)
18. Simplify and write the answer in scientific notation:
(4 x 10^-5)(3 x 10^0)/ (2 x 10^-2)(5 x 10^2)

Answer 1

17) a) Given that (-2x)^0

We have formula  that any thing to power 0 is 1.

(-2x)^0 = 1   [a^0 = 1]

b) Given that (-3x)^2

(-3x)*(-3x) = 9x^2

c) Given that 1/(6^-2)

= 36

 

Answer 2

16) 1/3y-1/2< 5/6y+1/2

Bring y varible terms to left side.

1/3y-5/6y <1/2+1/2

2y-5y/6 < 1

-3y/6 < 1

-y/2 < 1

Multiply each side by 2.

-y*2/2 = 1*2

-y < 2

Multiple to each side by negitive  one and change the symbol.

y > -2

17)a) (-2x)^0

Recall the formula a^0 = 1

(-2x)^0 = 1

b)(-3x)^2

= 9x^2

c)1/6^-2

1/a^-n = a^n

= 1/6^-2

=6^2

= 36

18)(4 x 10^-5)(3 x 10^0)/ (2 x 10^-2)(5 x 10^2)

a^0 =1 and a^n*a^-n = a^n-n = a^0 = 1

= (4x10^-5 *3x*1) /(2x*5x10^-210^2)

= (12x^210^-5)/10x^2

Cancell the possible terms

= 1210^-4