Final answer:
The expressions √49^8, √500, and √128 simplify to 7^8, 10√5, and 8√2, respectively. The value of x in the given equation is 3. The expression √12h^4 simplifies to 2h^2√3.
Step-by-step explanation:
To evaluate the following: √49^8 radical expression, we first recognize that √49 is 7, because 7×7 = 49. Therefore, √49^8 simplifies to 7^8.
To simplify √500, we find the prime factorization of 500 which is 2×2×5×5×5. We can take a pair of 2s and a pair of 5s out of the square root, which gives us 10√5 as the simplified form.
To determine the value of x that makes the equation -5x - (7 - 4x) = -2(3x - 4) true, first distribute the negatives through the parentheses: -5x - 7 + 4x = -6x + 8. Simplify this to -x - 7 = -6x + 8. Add 6x to both sides to get 5x - 7 = 8. Add 7 to both sides to get 5x = 15. Divide both sides by 5, so x = 3.
To simplify √12h^4, we note that √12 can be broken down to √(4×3) and √4 is 2. Since h^4 is a perfect square, it comes out of the square root as h^2. Thus, the simplified form is 2h^2√3.
To simplify √128, we find the prime factorization of 128 which is 2×2×2×2×2×2×2. Taking pairs of 2s out of the radical, we get 2×2×2×√2, which is 8√2.