# Thread: Need help with exponents: simplifying 3

1. ## Need help with exponents: simplifying 3

Ah thanks, I think I get it now. Just a couple more questions:

x^3 + x^-3 = does this equal x^0?

And:

(8a^-3b^6)^1/3 = is this 2a^-1b^2?

Thank you!!!!! sooo muchhh

2. Originally Posted by view360
Ah thanks, I think I get it now. Just a couple more questions:

x^3 + x^-3 = does this equal x^0?
no, the rule works for products, not sums.

$\displaystyle x^a \cdot x^b = x^{a + b}$

$\displaystyle x^a + x^b \ne x^{a + b}$

this is simply

$\displaystyle x^3 + \frac 1{x^3}$

now combine the fractions

And:

(8a^-3b^6)^1/3 = is this 2a^-1b^2?

Thank you!!!!! sooo muchhh
correct

EDIT: the princess' $\displaystyle \frac {2b^2}a$ is even nicer if you don't like negative powers.

3. Originally Posted by view360
Ah thanks, I think I get it now. Just a couple more questions:

x^3 + x^-3 = does this equal x^0?

And:

(8a^-3b^6)^1/3 = is this 2a^-1b^2?

Thank you!!!!! sooo muchhh
$\displaystyle x^3 + x^-3$ is not equal to x^0

$\displaystyle x^3 + \frac{1}{x^3}=x^0$

$\displaystyle \frac{x^6+1}{x^3}$not equal to x^0

(8a^-3b^6)^1/3 is not equal to 2a^-1b^2?
$\displaystyle \sqrt[3] {\frac{8b^6}{a^3}}$

$\displaystyle \frac{2b^2}{a}$