Simplify

[Sabi]

Any help with solving these would be really appreciated. I've had a go but I'm not confident with it.


(x^-4/5) / (x ^-7/5)

1/(x^4/5) / 1/(x^7/5)
x^(7/5-4/5)
x^(7+(-2^2/5)
x^3/5

√ y^6 / y

y^(6/2) / y
y^(2×3/2) / y
y^3 / y
y^(3-1)
y^2

2x(x)^4 / 4x √ x

2x^(1+4) / 4x√x
2x^5 / 4x√x
x^5 / 2x√x
x^4 / 2√x


3^x+2=6. Dont know where to start on this one, I believe it's with logs and I just get thrown by them so guidance would be great.

Many thanks to anyone kind enough to go through this.

 

[Dr.Peterson]

The first two answers are correct, but your work goes off in all directions rather than being direct. I would just say this:

(x^{-4/5}) / (x^{-7/5}) = (x^{-4/5}) * (x^{7/5}) = x^{-4/5 + 7/5} = x^{3/5}​

√(y^6) / y = (y^6)^{1/2} / y = y^{6 * 1/2} / y = y^3 / y^1 = y^{3-1} = y^2​

The third is well done, but you can go further:

x^4 / (2√x) = x^4 / (2*x^{1/2}) = ...​

The last is not about simplifying at all! It's an entirely different kind of problem: solving an equation. Yes, logs will be involved.

First isolate the exponential, by subtracting 2 from both sides. Then take the log (using any base you want), and simplify. Which base to use depends in part on whether you were asking for an exact answer, or a decimal approximation. Please state the entire problem, including instructions.