What is the simplified form of the expression?

(2x^6)(3x^1/2)
A.6x^13/2
B.6x^3
C.5x^13/2
D.5x^3
I got the answer 3x^7 but that's not one of the answer choices and I'm really lost.

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

= 2 * 3 * x^6 * x^1/2

= 6 * x^(6 + 1/2)

= 6 x^(12/2+1/2)

= 6 x^(13/2)

To simplify the expression (2x^6)(3x^1/2), you can use the properties of exponents and multiplication.

First, let's simplify the coefficient part. Multiply 2 by 3 to get 6.

Next, let's simplify the x terms. When you multiply variables with the same base (in this case, x), you can add their exponents. So, we add the exponents 6 and 1/2 for x.

6 + 1/2 = 6 + 0.5 = 6.5

Therefore, the simplified form of the expression is 6x^6.5.

However, since none of the answer choices match 6x^6.5, let's convert it to fractional exponent form:

To convert the decimal exponent 6.5 into fractional exponent form, you can write it as 6 1/2.

Now, we have 6x^(6 1/2).

Using the property of exponents, when you have an exponent raised to a power, you can multiply the exponents. So, we multiply 6 and 1/2.

6 * (1/2) = 6/2 = 3

Therefore, the simplified form of the expression is 6x^3, which matches option (B).

Keep in mind that it's important to double-check the answer choices to ensure there are no errors or typos.