Answer:
#43) 9^(1/2); #44) V = (1/3)^3 = 1/27
Step-by-step explanation:
#43) The only ways to make a power have a smaller value than the base is to use either a negative exponent (which we cannot do in this problem) or an exponent between 0 and 1 (a fraction or a decimal).
Finding a fractional power of a number is the same as taking that root of the number; for example, finding the 1/2 power of a number is the same as taking the square root; finding the 1/3 power of a number is the same as taking the cubed root; etc.
If we use 9 as the base (positive number) and 1/2 as the exponent (again a positive number), we would have 9^(1/2) = √9 = 3.
#44) To find the volume of any prism, find the area of the base and multiply it by the height.
For a cube, the base is a square; the area of a square is given by A = s², where s is the side length of the square.
Since the height of the cube will be the same as the length of the square (all sides are congruent in a cube), this makes the volume V = s²(s) = s³.
Since we know the side length is 1/3, this makes the volume
V = 1/3³ = 1/3(1/3)(1/3) = 1/9(1/3) = 1/27
