Final answer:
To find the value of q in the equation q^3 = 64, you need to calculate the cube root of 64, which is 4, because 4^3 equals 64.
Step-by-step explanation:
To find the value of q in the equation q3 = 64, you need to take the cube root of 64. When you take the cube root of a number, you are finding the value that, when multiplied by itself three times, gives you the original number. In this case, the cube root of 64 is 4, because 4 x 4 x 4 equals 64. Therefore, q = cube root of 64, which is 4.
It's important to understand that the cube root of a number is different from the square root, which is the number that, when multiplied by itself, gives you the original number. While the square root of a number is represented as the number to the power of one-half (x1/2), the cube root is represented as the number to the power of one-third (x1/3). Also, to explain negative exponents, they are equivalent to taking the reciprocal of the number raised to the positive exponent. So for instance, x-n = 1/xn.