Please help.... problem 1.) simplify (2y^2)^3/(4y^4)^2 and problem 2.) solve for t: s=(p+1)/t?

Question

How do you simplify/solve? Thanks so much for any help!

Answer 1

1) For the sake of legibility, I'll deal with each part of the fraction (before and after the / sign) separately:

(2y^2) ^ 3  = 8y^6

(4y^4)^2 =  8y^8

Because you're dividing, the 8s cancel out, leaving you with

y^6 and y^8.  When dividing two terms with the same base (just y in this case) you can just subtract the exponents.  

Hence the expression can be simplified as the difference of the two terms:

y^(6-8) = y^(-2)  which can also be written as

1/y^2

2) Perform the same operation to each side:

first, multiply by t to get

st = p+1

Then divide by s to get

t = (p+1) / s