Thread: Math 10 - Negative and Zero exponents

1. Math 10 - Negative and Zero exponents

The answer to this question is supposed to be 3; I can do half of the question, but then I get stuck.

Numerator: (6^4 + 4^6)^0
Denominator: 3^-1

From that I got:

Numerator: 2
Denominator: 3^-1

Then I did the flip thing to get rid of the negative exponent:

Numerator: 2
Denominator: 1/3^2

Then I simplified:

Numerator: 2
Denominator: 1/9

How can I simplify this further?

2. Originally Posted by t-dot
The answer to this question is supposed to be 3; I can do half of the question, but then I get stuck.

Numerator: (6^4 + 4^6)^0
Denominator: 3^-1

From that I got:

Numerator: 2
Denominator: 3^-1

Then I did the flip thing to get rid of the negative exponent:

Numerator: 2
Denominator: 1/3^2

Then I simplified:

Numerator: 2
Denominator: 1/9

How can I simplify this further?
Whoa! Hold on to those horses.

$\displaystyle \frac{(6^4 + 4^6)^0}{3^{-1}}$

Note that anything to the 0th power is 1. So the numerator is simply 1, not 2:
$\displaystyle = \frac{1}{3^{-1}}$

Now, a negative exponent either moves your number from the numerator to the denominator, or from the denominator to the numerator, so
$\displaystyle \frac{1}{3^{-1}} = \frac{3^1}{1} = 3$

-Dan

3. Woah dude, you did way too many steps. Anything to the 0 power is 1, so the numerator itself is simply 1, there's no need to do any other simplifying. For the denominator, 3^-1 on the denominator is the same as 3^1 on the numerator (basically, you are allowed to change the sign if you move something from the numerator to denominator or vice versa). As such, you're left with 3 * 1 which equals 3

*EDIT* Christ I was beat to the punch again lol

4. Thanks so much... i think i was just getting confused... and i wrote down the wrong number lol

5. Alright.... Umm New question

Numerator: 3^-3 +3^-4
Denominator: 3^-5

Do I have to flip ALL OF THESE??

This is what I got:

Numerator: 1/3^3 + 1/3^4
Denominator: 1/3^5

Then:

Numerator: 1/27 +1/81
Denominator: 1/243

How would you simplify this??
(Did I do too many steps again??)

6. Originally Posted by t-dot
Alright.... Umm New question

Numerator: 3^-3 +3^-4
Denominator: 3^-5

Do I have to flip ALL OF THESE??

This is what I got:

Numerator: 1/3^3 + 1/3^4
Denominator: 1/3^5

Then:

Numerator: 1/27 +1/81
Denominator: 1/243

How would you simplify this??
(Did I do too many steps again??)
You did good. Apparently (and not surprisingly if you're in 10th grade) you haven't done much yet with "complex fractions." Let me write out the steps of the problem:
$\displaystyle \frac{3^{-3} + 3^{-4}}{3^{-5}}$

$\displaystyle = \frac{\frac{1}{3^3} + \frac{1}{3^4}}{\frac{1}{3^5}}$

What you want to do here is multiply the numerator and denominator (of the "overall" fraction) by something that will get rid of the fractions in the numerator and denominator. The least common multiple of $\displaystyle 3^3, 3^4,3^5$ is obviously $\displaystyle 3^5$. So:
$\displaystyle \frac{\frac{1}{3^3} + \frac{1}{3^4}}{\frac{1}{3^5}} \cdot \frac{3^5}{3^5}$

$\displaystyle = \frac{\left ( \frac{1}{3^3} + \frac{1}{3^4} \right ) \cdot 3^5 }{\frac{1}{3^5} \cdot 3^5}$

$\displaystyle = \frac{\frac{1}{3^3} \cdot 3^5 + \frac{1}{3^4} \cdot 3^5}{1}$

$\displaystyle = 3^2 + 3 = 9 + 3 = 12$

-Dan

7. Thanks soo much .. that makes sooo much more sense!!!