Question

Please help I’m a bit confused on this I appreciate answers!

Answer 1

`(2x^3)^3=8\cdot x^(9)`

Explanation:

Properties of Exponents

The property called Power to a Power shows us how to simplify expressions of the type:

`(x^n)^m=x^(n*m)`

Similarily the property called Power of a product simplifies expressions like:

`(x.y)^n=x^n.y^n`

The company mentioned in the question uses the expression

`(2x^3)^3`

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:

`(2x^3)^3=2^3\cdot (x^3)^3`

Now use the power to a power property:

`(2x^3)^3=2^3\cdot x^(3*3)`

Operate:

`\mathbf{(2x^3)^3=8\cdot x^(9)}`