Problem 46 - College Algebra Essentials

Question

Simplify each exponential expression. $$\left(11 x^{5}\right)\left(9 x^{12}\right)$$

Step-by-Step Solution

Answer

The simplified form of the given exponential expression is \(99x^{17}\).

Step 1: Observe the Expression

Look at the expression: \( (11x^{5})(9x^{12}) \). It consists of two parts: coefficients (11 and 9) and exponential terms (\(x^{5}\) and \(x^{12}\)). These parts need to be handled separately.

Step 2: Multiply the Coefficients

Multiply the coefficients: \(11 \times 9 = 99\). This will be the new coefficient on the \(x\) variable.

Step 3: Add Exponents

When multiplying exponential expressions with the same base, we add the exponents together, as stipulated by the law of exponents. So, do \(5 + 12 = 17\) to add the two exponents of \(x\).

Step 4: Write down the Final Solution

Combine the results of steps 2 and 3 to form the final solution: \(99x^{17}\). This is the simplest form the original expression can be written in.