Simplify:

-4(x^2)^7(w^8)^3
22x^6(w^10)^3 z

2. Originally Posted by Elli
Simplify:

-4(x^2)^7(w^8)^3
22x^6(w^10)^3 z
This is the same as saying $\displaystyle -\frac{4}{22}\cdot\left(\frac{x^{14}}{x^6}\right)\c dot\left(\frac{w^{24}}{w^{30}}\right)\cdot\left(\f rac{1}{z}\right)$

Do you think you can simplify this now?

3. Thanks, Chris

-2x^8w^6
11z

but my answers give me w^-6 "under the line"

4. Originally Posted by Elli
Thanks, Chris

-2x^8w^6
11z

but my answers give me w^-6 "under the line"
Note that $\displaystyle \frac{w^{24}}{w^{30}}=w^{24-30}=w^{-6}=\frac{1}{w^6}$

5. so, how do you know when it goes "underline" or above?

the w6

6. Originally Posted by Elli
so, how do you know when it goes "underline" or above?

the w6
Hello Elli,

When you have a variable with exponent in the numerator and same variable with exponent in the denominator, subtract the exponents (numerator exponent - denominator exponent).

If the result is positive, leave the variable with the new exponent in the numerator. If the exponent is negative, put the variable with new exponent in the denominator.

See Chris's last example.

$\displaystyle \frac{w^{24}}{w^{30}}=w^{-6}=\frac{1}{w^6}$

When he subtracted 24-30, the result was -6. So he put the $\displaystyle w^6$ in the denominator.