Final answer:
The expression 0.008b^6 can be expressed as the cube of a monomial by taking the cube root of the numerical coefficient 0.008, which is 0.2, and dividing the exponent 6 by 3 for the variable b, which gives b^2. Therefore, the expression in the form of a cube is (0.2b^2)^3.
Step-by-step explanation:
To express the number 0.008b^6 as the cube of a monomial, we need to find a monomial that, when cubed, will yield this expression. We start by taking the cube root of the coefficient and the variable separately.
Cubing of exponentials works by cubing the numerical coefficient and then applying the cube to the variable with its exponent. In this case, the cube root of 0.008 is 0.2, because (0.2)3 = 0.008. Similarly, to find what needs to be cubed to give us b6, we divide the exponent by 3, giving us b2 because (b2)3 = b6.
Therefore, the expression 0.008b^6 as a cube of a monomial is:
(0.2b^2)^3