Question

friday
simplify each of the following.
$(9ab^2)^0 \cdot (2c^3)^6 =$

Explanation:

Step1: Simplify \((9ab^2)^0\)

Any non - zero number or expression raised to the power of 0 is 1. Since \(9ab^2\) is non - zero (assuming \(a\), \(b\) are not such that the expression is zero), \((9ab^2)^0 = 1\).

Step2: Simplify \((2c^3)^6\)

Using the power of a product rule \((xy)^n=x^n y^n\) and the power of a power rule \((x^m)^n=x^{mn}\), we have:
First, apply the power of a product rule: \((2c^3)^6=2^6\times(c^3)^6\)
Then, calculate \(2^6 = 64\) and \((c^3)^6=c^{3\times6}=c^{18}\)
So, \((2c^3)^6 = 64c^{18}\)

Step3: Multiply the two simplified expressions

We have \((9ab^2)^0\cdot(2c^3)^6=1\times64c^{18}\)

Answer:

\(64c^{18}\)