Negative fraction with exponent?

**Mesoc** · January 28th 2011, 11:20 AM

The negative sign is confusing. Granted it's like *-1, but with the exponent, i don't know how it should look. I have a test coming up, and these are a couple of practice ones that I got. Please let me know if I'm on the right track.

1)

-4^5
------
-4^2 =-4^3 = (-4) (-4) (-4) = -64 ???

2)

( 2 )^3
- (-----)
( 3 )

= (-1) (-2) (-2) (-2) = 8
-----
= (-1) (-3) (-3) (-3) = 27 ???

Thanks

**pickslides** · January 28th 2011, 11:40 AM

Hi there Mesoc,

Originally Posted by Mesoc

1)

-4^5
------
-4^2 =-4^3 = (-4) (-4) (-4) = -64 ???

Which one is your equation?

$\displaystyle\frac{-4^5}{-4^2} = -4^{5-2} = -4^3 = -(4\times 4\times 4) = -64$

$\displaystyle \frac{(-4)^5}{(-4)^2} = (-4)^{5-2} = (-4)^3 = -4\times -4\times -4 = -64$

You won't always get the same answer!

Originally Posted by Mesoc

2)

( 2 )^3
- (-----)
( 3 )

= (-1) (-2) (-2) (-2) = 8
-----
= (-1) (-3) (-3) (-3) = 27 ???

Just guessing again,

$\displaystyle -\left(\frac{2}{3} \right)^3 = -\left(\frac{2^3}{3^3} \right) = \frac{-8}{27}$

**e^(i*pi)** · January 28th 2011, 11:59 AM

The minus sign is largely the same as multiplying by -1. So $-a = -1 \cdot a$

When you have an exponent you can do that and then use the law $(ab)^c = a^cb^c$ although it only works if the minus sign is part of the base being raised. If it's outside the brackets then you act upon it after the exponent

For example $(-2)^2 = (-1 \cdot -2)^2 = (-1)^2 \cdot (-2)^2 = +4$ whereas $-(2^2) = -1 \cdot 4 = -4$

You should always use brackets to make it clear which case you mean

**Mesoc** · January 28th 2011, 07:53 PM

[QUOTE=pickslides;610788]Hi there Mesoc,

Which one is your equation?

$\displaystyle\frac{-4^5}{-4^2} = -4^{5-2} = -4^3 = -(4\times 4\times 4) = -64$

You won't always get the same answer!

^ that's the equation. They love throwing these negatives in to screw with us.

Just guessing again,

$\displaystyle -\left(\frac{2}{3} \right)^3 = -\left(\frac{2^3}{3^3} \right) = \frac{-8}{27}$ [/QUOTE

That's correct, but stupid question...why is there a negative in front of the 8, instead of the fraction? or does it not matter?

----

Thanks ei, that cleared up a rule i was unsure of.

**dwsmith** · January 28th 2011, 07:54 PM

[QUOTE=Mesoc;610922]

Originally Posted by pickslides

Hi there Mesoc,

Which one is your equation?

$\displaystyle\frac{-4^5}{-4^2} = -4^{5-2} = -4^3 = -(4\times 4\times 4) = -64$

You won't always get the same answer!

^ that's the equation. They love throwing these negatives in to screw with us.

Just guessing again,

$\displaystyle -\left(\frac{2}{3} \right)^3 = -\left(\frac{2^3}{3^3} \right) = \frac{-8}{27}$ [/QUOTE

That's correct, but stupid question...why is there a negative in front of the 8, instead of the fraction? or does it not matter?

----

Thanks ei, that cleared up a rule i was unsure of.

Doesn't matter.

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