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.