Question

Simplify (3x^2y^5)^3

Answer 1

the answer is b, 27x^6y^15

Answer 2

Answer: Choice B

Work Shown:

`\left(3\text{x}^2\text{y}^5\right)^3\\\\\left(3\right)^3\left(\text{x}^2\right)^3\left(\text{y}^5\right)^3\\\\27\text{x}^(2*3)\text{y}^(5*3)\\\\27\text{x}^(6)\text{y}^(15)\\\\`

Step-by-step explanation:

The outer exponent 3 is "distributed", so to speak, to each term inside the parenthesis. This isn't the actual distribution rule. But we can think of it as such. This is what's happening in the second step.

So we'll cube the coefficient 3 to get 3^3 = 27, and we'll cube x^2 to get x^6, and finally cube y^5 to get y^15.

I used the rule
`(a^b)^c = a^(b*c)` for the third step.