Answer:
[tex](2x^3)^3=8\cdot x^{9}[/tex]
Step-by-step explanation:
Properties of Exponents
The property called Power to a Power shows us how to simplify expressions of the type:
[tex](x^n)^m=x^{n*m}[/tex]
Similarily the property called Power of a product simplifies expressions like:
[tex](x.y)^n=x^n.y^n[/tex]
The company mentioned in the question uses the expression
[tex](2x^3)^3[/tex]
millimeters per second to calculate the maximum capacity of a photocell with an area of x^3 square millimeters.
First, use the power of a product property:
[tex](2x^3)^3=2^3\cdot (x^3)^3[/tex]
Now use the power to a power property:
[tex](2x^3)^3=2^3\cdot x^{3*3}[/tex]
Operate:
[tex]\mathbf{(2x^3)^3=8\cdot x^{9}}[/tex]
