Problem 29 - Algebra and Trigonometry

Question

Simplify each exponential expression. $$x^{-5} \cdot x^{10}$$

Step-by-Step Solution

Answer

\(x^{5}\)

Step 1: Identify the base and the exponents

In this exercise, the base (which is the number that is being multiplied) is \(x\), and the exponents are \(-5\) and \(10\). The exponential expression we are simplifying is \(x^{-5} \cdot x^{10}\).

Step 2: Apply the law of exponents

The law of exponents states that when multiplying expressions with the same base, the exponents should be added together. So we can rewrite \(x^{-5} \cdot x^{10}\) as \(x^{-5 + 10}\).

Step 3: Simplify the expression

Finally, simplify the expression by performing the addition in the exponent. The result is \(x^{5}\).