Problem 33 - College Algebra Essentials

Question

Simplify each exponential expression. $$\left(x^{-5}\right)^{3}$$

Step-by-Step Solution

Answer

The simplified form of the given expression \( (x^{-5})^{3} \) is \( x^{-15} \)

Step 1: Identify the given expression

First identify the problem at hand. Here, we have an exponential expression \( (x^{-5})^{3} \), which we need to simplify.

Step 2: Apply the Power of a Power Rule

Apply the power of a power rule which states that when a power is raised to another power, you multiply the exponents. In our case, the base is \( x \) with an exponent of -5. This is raised to the power of 3. We multiply the exponents -5 and 3 to get \( x^{(-5*3)} \)

Step 3: Simplify the expression

After multiplying the exponents, simplify the expression. Here, \( -5*3 = -15 \), therefore the expression simplifies to \( x^{-15} \)