The dimensions of Ashley's sandbox are c^3 by c^5 by 4v^5. Which of the following expressions represents the volume of the sandbox?

Question

1. 4c^15 v^5
2. 20c^15 v^5
3. 4c^8 v^5
4. 2c^8 v^5

Answer 1

The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.

Given that the dimensions of Ashley's sandbox are c^3 by c^5 by 4v^5, the volume would be V = c^3 * c^5 * 4v^5.

To simplify this expression, we can use the properties of exponents. When multiplying with the same base, we add the exponents. Additionally, we can multiply the coefficients.

First, let's simplify the base with exponents:
c^3 * c^5 = c^(3+5) = c^8

Then, we have:
V = c^8 * 4v^5

Finally, multiplying the coefficient and the base with exponents, we get:
V = 4c^8 * v^5

Therefore, the volume of Ashley's sandbox is represented by the expression 4c^8 v^5.

So, the correct answer is option 3.