answer:Using the properties of exponents, we can simplify (2^2)^3 as 2^{2 cdot 3}. Simplifying further, we get 2^6. Evaluating 2^6, we find that (2^2)^3 is equal to boxed{64}. The answer is: 64

answer:Sue has 7 purple beads. She has twice as many blue beads as purple beads, so she has 7 x 2 = 14 blue beads. She also has 11 more green beads than blue beads, so she has 14 + 11 = 25 green beads. The total number of beads in the necklace is 7 + 14 + 25 = 46 beads. 46 The answer is: 46

answer:Since x is a positive multiple of 8, we can write x=8k for some positive integer k. We are given that x^2>100, so (8k)^2>100. Simplifying, we have 64k^2>100. Dividing both sides by 64, we get k^2>frac{100}{64}. Since k is a positive integer, we have k^2geq leftlceilfrac{100}{64}rightrceil=2. Therefore, the smallest possible value of k is sqrt{2}, and since k is a positive integer, we take k=2. Thus, x=8k=8(2)=boxed{16}. The answer is: 16

answer:we need to solve the equation g(x) = X. Let's substitute the given solutions into the equation and see if they satisfy the equation. For x = -1: g(-1) = 3(-1) + 6 = 3 - 6 = -3 So, g(-1) = -3, which is not equal to X. For x = 8: g(8) = 2(8) - 13 = 16 - 13 = 3 So, g(8) = 3, which is not equal to X. Neither of the given solutions satisfy the equation g(x) = X. Therefore, based on the given information, we cannot determine the value of X. The answer is: 3