how do I simplify the square root of 49 x to the 6th power?

square root means 1/2 exponent,

so we can write the above problem as (49x⁶)^1/2

^{now distribute that exponent 1/2 on each term inside the parenthesis,}

so now we will hve (49)^1/2 (x⁶)^1/2

(7²)^1/2 (x)6/2

(7)^2/2 (x³)

(7)¹ (x³)

7x³ 

so 7x³ is the answer.

We actually need to include an absolute value here, because the "x"  under the radical could be negative......so........the complete answer is    7 l x^3 l