Problem 48 - College Algebra Essentials

Question

Simplify each exponential expression. $$\left(-5 x^{4} y\right)\left(-6 x^{7} y^{11}\right)$$

Step-by-Step Solution

Answer

The simplified form of \(-5x^{4}y * -6x^{7}y^{11}\) is \(30x^{11}y^{12}\).

Step 1: Multiply the numerical coefficients

The numerical coefficients are -5 and -6. Multiply these two numbers to get 30.

Step 2: Add the exponents of x

The powers of x are 4 and 7. Since the bases (x) are the same, the powers should be added. \(x^{4} * x^{7} = x^{4+7} = x^{11}\)

Step 3: Add the exponents of y

The powers of y are 1 and 11. Since the bases (y) are the same, the powers should be added. \(y^{1} * y^{11} = y^{1+11} = y^{12}\)

Step 4: Combine all parts

Multiply the numerical part (30) with the variables, x and y. This results in \(30x^{11}y^{12}\).