# Thread: Exponents

1. ## Exponents

My teacher decided that we needed a review and hit us with Exponents. Well seems he was right. I'm having trouble remembering and simplifying exponents.

The only rules for the problems he's given us is "Leave without radicals or negative exponents"

1. (.1)^2(4xy^2)^2

For this one I...

.01(16x^2y^4)

But from here I forget what to do. Do I distribute the .01 to 16, x^2, and y^4?

The second one I'm having trouble is

3(3^(x/2))^2

Correct me if I'm wrong please...

3(9x^2)

27x^2

Thanks any help is greatly appreciated

2. 1. (.1)^2(4xy^2)^2

For this one I...

.01(16x^2y^4)

But from here I forget what to do. Do I distribute the .01 to 16, x^2, and y^4?

Good question, the distributing to all?

But the answer is no. Since 0.01 is a constant, and there is also a constant---16---in the (16 x^2 y^4), then just multiply the 0.01 to the 16.
= 0.16 x^2 y^4.

Suppose it is y(16 x^2 y^4)?
Are you going to multiply y each to 16, x^2 and y^4?
No. To the y^4 only.
See?

Edit:

Now, if it were (0.01)(16 +x^2 +y^4)
then you have to multiply the 0.01 to each of the 3 terms inside the parentheses.

-----------------------------------

3(3^(x/2))^2

= 3[(3^(x/2))^2]
= 3[3^(x/2 *2)]
= 3[3^x]
= [3^1]*[3^x]
= 3^(x+1) ------------answer.

We used:
----(a^b)^c = a^(b*c)
Example, (3^2)^3 = 3^(2*3) = 3^6 = 729.
Check, (3^2)^3 = 9^3 = 729 -----same, so, OK.

----(a^b)*(a^c) = a^(b+c)
Example, (3^2)(3^3) = 3^(2+3) = 3^5 = 243.
Check, (3^2)(3^3) = 9(27) = 243 also, so, OK.