## calculusxy one year ago help with exponents. question below.

1. calculusxy

$\large \frac{ (-u^3)^3 }{ u^{-2}v^4 \times -2v^0\times-2u^3v^4 }$

2. calculusxy

@Nnesha @phi

3. Owlcoffee

Do you want to simplify it?

4. calculusxy

yes

5. calculusxy

$\frac{ u^9 }{ u^{-2}v^4\times-2v^0\times-2u^3v^4 }$

6. Owlcoffee

Okay, in other words, the expression looks like this: $\frac{ (-u^3)^3 }{ u ^{-2}v^4(-2v^0)(-2u^3v^4) }$

7. calculusxy

i meant to put a -u^9

8. Owlcoffee

Let's begin by working with the denominator, let's associate all the "v"s and "u"s together sice this does work through the axiom of associative and commutative of multiplication: $a.b=b.a$ $a(c.b)=(a.c)b$ So, let's associate the denominator in order to make things clearer: $\frac{ -u^9 }{ (-2)(u ^{-2})(u^3)(-2)(v^0)(v^4)(v^4) }$ That -2 x -2 can be represented as 4 so: $\frac{ -u^9 }{ (4)(u ^{-2})(u^3)(v^0)(v^4)(v^4) }$ Now, let's make use of a useful property which has this form: $$a^ma^n=a^{m+n}$$ This will allow us to operate those exponents: $\frac{ -u^9 }{ (4)(u ^{(-2)+3})(v ^{0+4+4}) }$