Question

Which expression is equivalent to 45m^-6 p^2 v^12 / 15m^-2 p^8 v^-4 for all values of m, p, and v where the expression is defined?

Answer 1

To simplify the given expression, divide the numerical coefficients and apply the rules of exponents to the variables. The final simplified expression is 3m^-4 p^-6 v^16.

Step-by-step explanation:

To simplify the expression 45m-6 p2 v12 / 15m-2 p8 v-4, we need to apply the rules of exponents and perform the necessary multiplications and divisions.

First, let's simplify the numerical coefficients:

• 45 / 15 = 3

Next, let's simplify the variables:

• m-6 / m-2 = m-6 - (-2) = m-4
• p2 / p8 = p2 - 8 = p-6
• v12 / v-4 = v12 - (-4) = v16

Combining all the simplified terms, we get:

• 3m-4 p-6 v16