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Chapter 0: Problem 33

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

Short Answer

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

Step by step solution

01

Identify the given expression

First identify the problem at hand. Here, we have an exponential expression \( (x^{-5})^{3} \), which we need to simplify.
02

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 \( x^{(-5*3)} \)
03

Simplify the expression

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

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