maths help?

Here's how we'd break that down in my pre-algebra class.
1. y=5
y2=5*2 which equals 10

2. y=7
7*7*7*7=2,401

3.y=7
1,000/7 equals 0.007

Hope that's helpful.
I double checked my answers with my pc's calc.

-Sarah-

y^2 = 10

y^4 = 10^2 = 100

y^x = 1000
y^x = y^6
x = 6

y^2=10
y=sqrt. 10
y=3.16

y^4=99.71

first solve for "y" in the first equation

y^2 = 10, sqrt both sides
√ y^2 = √10, simplify
y = √10

the second equation is to plug in √10 for y

y^4 = x
√10^4 = x
√1000 = x
100 = x, answer

y^x = 1000, plug in y
√10^x = 1000, square both sides
10^x = 1000^2
x*log10 = 2*log 1000, add log to get x out of the exponential form

x = 2*log1000 / log 10
i don't have a calculator on me so... you got to do the final step

If you're given y^2=10, y=Sqrt[10]=10^1/2

y^4 = (10^1/2)^4 = 10^2=100

y^x=1000
(10^1/2)^x=1000
10^x/2=1000

Log 10^x/2 = Log 1000
x/2=3
x=6
y^6=1000

y^4 = (y^2)^2 = 100
100 * 10 = 1000 = y^4 * y^2 = y^6