Which expression is equivalent to (7x^3)^2(x^8)^1/2?
A. 14x^10
B. 49x^10
C. 14x^7
D. 49x^7
To find the equivalent expression, we start by simplifying each term inside the parentheses.
First, we have (7x^3)^2. To simplify this, we square the base and multiply the exponents, giving us 7^2*x^(3*2) = 49x^6.
Next, we have (x^8)^1/2. To simplify this, we take the square root of x^8, which gives us x^(8/2) = x^4.
Now we can substitute these simplified terms back into the original expression:
(7x^3)^2(x^8)^1/2 = (49x^6)(x^4) = 49x^6 * x^4 = 49x^(6+4) = 49x^10.
So the equivalent expression is 49x^10, which corresponds to choice B.