Math Help - take a power of -1 out

1. take a power of -1 out

Just a quickie...

is

$(-\frac{2}{4}u^{-4}-\frac{7}{5}u^{-5}) = -\frac{1}{20}u^{-4}(10+28u^{-1})$

correct?

2. yes.

3. yes your correct due to rules of indices i.e. $u^{-4}.u^{-1} = u^{-4+(-1)} = u^{-5}$

4. Hello, darksupernova!

$\left(-\frac{2}{4}u^{-4}-\frac{7}{5}u^{-5}\right) \;=\; -\frac{1}{20}u^{-4}(10+28u^{-1})$

Correct?

Assuming that the instructions are: "Factor completely" . . .

When factoring out a variable, we factor out the "least exponent".

Example: . $4x^5 + 7x^3 \:=\:x^3(4x^2 + 7)$

. . . . . . . Otherwise, we could claim that:
. . . . . . . $x(4x^4 + 7x^2)\,\text{ and }\,x^2(4x^3 + 6x)$ are both correct.

Also, the LCD of $\frac{1}{2}$ and $\frac{7}{5}$ is 10.

Preferred answer: . $-\frac{1}{10}u^{-5}(5u + 14)$

5. thank you very much