I just want to see if my answers are correct and if no, can you please show your work and explain how to do it? Thank you.

A. (x^1/2)^4√x^6
I got an answer of x^2x
B. √x^4y^12
I got an answer of xy
C. 3√a^6b^3
I got an answer of a^2b
D. (x^1/3y)^3√x^2y^2
I got an answer of xy^4xy
E. (x^1/4)^8/3√x^3
I got an answer of x
And how do you write an expression in exponential form?
For example: 3√b^4 or 4√256b^5?

Ms. Sue can you please help?

A. (x^1/2)^4√x^6

x^2 x^3 = x^5

B. I do not know if you mean
(x^4)^.5 y^12
or
(x^4 y^12)^.5
if the second then
x^2 y^6

C if you mean
(a^6 b^3)^1/3
then indeed
a^2 b

I am at a loss with your notation

thank you yes it is hard to explain

Sure! Let's go through each of the expressions and check your answers:

A. (x^(1/2))^4√x^6

To simplify this expression, we need to multiply the exponents and combine the radicals:

(x^(1/2))^4 = x^(1/2 * 4) = x^2

√x^6 = (x^6)^(1/2) = x^(6 * 1/2) = x^3

Therefore, the simplified expression is x^2 * x^3 = x^5, so your answer of x^2x is incorrect.

B. √x^4y^12

To simplify this expression, we apply the square root separately to each term:

√x^4 = (x^4)^(1/2) = x^(4 * 1/2) = x^2

√y^12 = (y^12)^(1/2) = y^(12 * 1/2) = y^6

Therefore, the simplified expression is x^2 * y^6 = x^2y^6, so your answer of xy is incorrect.

C. 3√a^6b^3

To simplify this expression, we take the cube root of each term separately:

3√a^6 = (a^6)^(1/3) = a^(6 * 1/3) = a^2

3√b^3 = (b^3)^(1/3) = b^(3 * 1/3) = b^1 = b

Therefore, the simplified expression is a^2 * b = a^2b, so your answer of a^2b is correct.

D. (x^(1/3)y)^3√x^2y^2

To simplify this expression, we apply the cube root to x^(1/3)y and then multiply all the exponents together:

(x^(1/3)y)^(3 * 1/3) = (x^(1/3)y)^(1) = x^(1/3 * 1) * y^(1/3 * 1) = x^(1/3) * y^(1/3)

(√x^2y^2)^(3/2) = (x^2y^2)^(3/2) = x^(2 * 3/2) * y^(2 * 3/2) = x^3 * y^3

Therefore, the simplified expression is (x^(1/3) * y^(1/3)) * (x^3 * y^3) = x^(1/3 + 3) * y^(1/3 + 3) = x^(10/3) * y^(10/3), so your answer of xy^4xy is incorrect.

E. (x^(1/4))^(8/3)√x^3

To simplify this expression, we simplify the exponents first and then multiply:

(x^(1/4))^(8/3) = x^((1/4) * (8/3)) = x^(2/3)

√x^3 = (x^3)^(1/2) = x^(3 * 1/2) = x^(3/2)

Therefore, the simplified expression is x^(2/3) * x^(3/2) = x^(2/3 + 3/2) = x^(11/6), so your answer of x is incorrect.

Now, to answer your question about writing an expression in exponential form:

To write an expression in exponential form, you need to convert various operations and radicals into exponents. For example:

1. 3√b^4 can be written as b^(4/3)
2. 4√(256b^5) can be written as (256b^5)^(1/4)

In general, if you have the nth root of a term raised to the power of m, it can be written as the term raised to the power of m/n.

I hope this explanation helps you understand the concepts better! Let me know if you have any further questions.