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.