# Thread: Simplifying expressions involving exponents

1. ## Simplifying expressions involving exponents

The first question is
1. Simplify without negative exponents
-7x^-2
Now doing this one I had trouble, the answer I came up with was 1/7x^2

2. Simplyfy without negative exponents
x^-7/x^2
This was my reasoning x^-7+2=x^-5=1/x^5
I guess I got it wrong though?

3. Simplify using positive exponents
(-4v^7/3)(2v^-1/3)
I did (-4)(2) (v^7/3+-1/3)= -8v

4. Simplify using positive exponents
3x^2/3/7x
I got 3/7x^1/3

2. $-7x^{-2} = -\frac{7}{x^2}$
$\frac{x^{-7}}{x^2} = (x^{-7})(x^{-2}) = x^{-9} = \frac{1}{x^9}$
$(-4v^{\frac{7}{3}})(2v^{-\frac{1}{3}}) = 8v^{\frac{7}{3} - \frac{1}{3}} = -8v^{\frac{6}{3}} = -8v^2$
$\frac{3x^{\frac{2}{3}}}{7x} = \frac{3}{7}x^{-\frac{1}{3}} = \frac{3}{7x^{\frac{1}{3}}}$