Find the product.

(-5a^2)^3·a^5

Question

Find the product.

(-5a^2)^3·a^5

whpalmer4 · Answer

Here you get another property of exponents:

$$(ab)^n = a^nb^n$$

So you can rewrite the first part as
$$(-5a^2)^3 = (-5)^3(a^2)^3$$

and use what you learned on the previous problem to do the rest.

anonymous · Answer

I tried solving it and my answer didn't fit with the answers provided... That's why I posted it. x) I'm not very good at this. Hoping someone could help me with the answer. Maybe walk thru how to do it?

whpalmer4 · Answer

Okay, that's what I'm trying to do, but perhaps the math notation isn't clear to you.  

Continuing on from where I left off, can you figure out the value of $(-5)^3$?

whpalmer4 · Answer

Hint: it's the same as (-5)(-5)(-5)

anonymous · Answer

So, -125?

whpalmer4 · Answer

Very good.  So now we have 
$$(-5a^2)^3 *a^5 = -125 (a^2)^3 a^5$$Can you simplify $(a^2)^3$?

whpalmer4 · Answer

Hint:
$$(a^n)^m = a^{n*m}$$

anonymous · Answer

a^6?

whpalmer4 · Answer

Yes!  If that doesn't make complete sense to you, look at it this way:

$$(a^2)^3 = (a*a)^3 = (a*a)*(a*a)*(a*a) = a*a*a*a*a*a = a^6$$

whpalmer4 · Answer

Now we've got $(-5a^2)^3*a^5 = -125a^6a^5$ Can you finish the simplification?

whpalmer4 · Answer

Here the visual model would be 
$$a^6a^5 = (a*a*a*a*a*a)*(a*a*a*a*a)$$$$ = a*a*a*a*a*a*a*a*a*a*a = a^?$$

anonymous · Answer

-125a^11???

whpalmer4 · Answer

That's the final answer, yep!

anonymous · Answer

Thank you so much!!! :D

whpalmer4 · Answer

They aren't really that hard, it just takes some practice (and attention to detail).  

Here's one for you, let's see if you can build on what you've learned:

What is $((a^2)^3)^4$?

anonymous · Answer

a^24?

whpalmer4 · Answer

Ding ding ding!  We have a winner!

anonymous · Answer

Yay! I wish you were my actual teacher. She left us with a sub that doesn't know like... Anything! And my teacher isn't much help. She's just like, "Here's the problem, here's the answer."

anonymous · Answer

You helped me understand!

whpalmer4 · Answer

Great!  That's always my goal :-)  It's nice working with people who want to understand, not just have an answer to put into their computer...

anonymous · Answer

Thank you @whpalmer4. You're such a great teacher!

whpalmer4 · Answer

Thanks, you made my day!

anonymous · Answer

I'm glad! :D