Question

Which expression is equivalent to √(8x^7y^8) assuming x > 0?

A) 2x^3y^4√2x

B) 2xy^4√2x^3

C) 2x^3y^4√2

D) 2√x^3y^4√2

Answer 1

The expression √(8x^7y^8) is equivalent to 2x^(7/2) * y^(4)√2x.

Step-by-step explanation:

The expression √(8x^7y^8) can be simplified by using the rule of exponents that says √(ab) = √a * √b. Applying this rule, we can write the expression as √(8) * √(x^7) * √(y^8). The square root of 8 can be simplified to 2√2. The square root of x^7 can be written as x^(7/2) and the square root of y^8 can be written as y^(8/2). Simplifying further, we get 2√2 * x^(7/2) * y^(8/2). Combining like terms, the equivalent expression is 2x^(7/2) * y^(4). Therefore, option A) 2x^3y^4√2x is the correct answer.