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Chapter 10: Problem 44

Simplify the expression. $$\left(\frac{z}{2}\right)^{3}$$

Short Answer

Expert verified
\(\frac{z^3}{8}\)

Step by step solution

01

Identify the expression

The given expression to simplify is \(\bigg(\frac{z}{2}\bigg)^{3}\).
02

Apply the power rule

Use the power rule for exponents, which states \(\bigg(\frac{a}{b}\bigg)^{n} = \frac{a^n}{b^n}\). Here, \(a = z\), \(b = 2\), and \(n = 3\).
03

Simplify the expression

Applying the power rule: \(\bigg(\frac{z}{2}\bigg)^{3} = \frac{z^3}{2^3} = \frac{z^3}{8}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Power Rule
The power rule is an important principle in mathematics, especially when dealing with exponents. The rule states that if you have a fraction raised to a power, you can apply that power to both the numerator and the denominator. This can be expressed as \(\bigg(\frac{a}{b}\bigg)^{n} = \frac{a^n}{b^n}\). Let's break it down:
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