Need Help with These Exponential Equations

Hello there!

I recently enrolled in a high school math course needed to take a college course, but I was always dreadful at math, and this is a correspondence course with minimal student assistance.

I am having some difficulties, and would like help with two question

1)

(3x^{4}*y^{5}*z^{7})^{5 }___________

(-3x^{3}*yz^{4})^{7}

For this question I got

y^{18}z^{7}

_____

9x

However I think I am wrong. The next question I found even more confusing

2)

(x^{a+b})^{a-b}

_________

(x^{a-2b})^{a+2b }

for this one I got 1/-4 but again, i think I am very lose

Re: Need Help with These Exponential Equations

Quote:

Originally Posted by

**Reiper** Hello there!

I recently enrolled in a high school math course needed to take a college course, but I was always dreadful at math, and this is a correspondence course with minimal student assistance.

I am having some difficulties, and would like help with two question

1)

(3x^{4}*y^{5}*z^{7})^{5 }___________

(-3x^{3}*yz^{4})^{7}

For this question I got

y^{18}z^{7}

_____

9x

However I think I am wrong. The next question I found even more confusing

2)

(x^{a+b})^{a-b}

_________

(x^{a-2b})^{a+2b }

for this one I got 1/-4 but again, i think I am very lose

You are close with the first, just remember that $\displaystyle \displaystyle \begin{align*} (-3)^7 = -3^7 \end{align*}$, so your answer should be negated.

I'm afraid you're not even close with the second. You need to use the following: $\displaystyle \displaystyle \begin{align*} \left(a^p\right)^q = a^{pq} \end{align*}$ and $\displaystyle \displaystyle \begin{align*} \frac{a^{m}}{a^n} = a^{m - n} \end{align*}$

Re: Need Help with These Exponential Equations

(x^{a+b})^{a-b}

so here is what I am not getting, why do you not just multiply the exponents? IE (a+b)(a-b) = (a^{2}-b^{2})

and if I do (x^{a+b}) = (x^{a}x^{b}, then where do I go from there with the exponents outside the bracket?

could someone show me what step 2 and three of this question would look like?

Re: Need Help with These Exponential Equations

$\displaystyle \frac{(x^{a+b})^{a-b}}{(x^{a-2b})^{a+2b}}$

$\displaystyle \frac{x^{a^2-b^2}}{x^{a^2-4b^2}}$

$\displaystyle x^{(a^2-b^2) - (a^2-4b^2)}$

$\displaystyle x^{3b^2}$