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When dealing with expressions that involve exponents, one handy power rule to remember is the exponent distributive property. This rule tells us that when a product of numbers is raised to an exponent, each factor in the product should be raised to that exponent separately. Consider the expression

• your current expression: \((4u)^3\)
• The exponent of 3 gets distributed to each factor in the bracket:

\( (4u)^3 = 4^3 \times u^3 \)
This property helps break down complex expressions into simpler parts, making them more manageable to solve.
By applying this rule, you ensure each component is correctly elevated to the power, resulting in an accurate and simplified result.

Simplifying expressions is a crucial skill in algebra. It involves breaking down complex expressions into their simplest form. Once we've applied the exponent distributive property to \((4u)^3\), we have the equivalent expression: \(4^3 \times u^3\). To simplify this:

• Calculate the value of \(4^3\). Raise 4 to the power of 3, which means multiplying 4 by itself three times: \(4 \times 4 \times 4 = 64\).
• For the term \(u^3\), write it as \(u \times u \times u\).

Combining these results, you end up with the simplified expression: \(64u^3\). Breaking expressions into smaller parts and reconciling them helps further streamline the solving process.

Algebraic expressions are fundamental components of algebra. These expressions consist of numbers, variables, and mathematical operators. For example, \((4u)^3\) involves both constants (the number 4) and variables (the letter \(u\)). Understanding and manipulating algebraic expressions is essential for solving various math problems.
Within an algebraic expression, variables represent unknown values that can change. Operations like addition, subtraction, and multiplication connect these numbers and variables. When given a scenario, combining and simplifying these elements lets you find solutions more effectively.
By mastering how to work with and simplify algebraic expressions, you develop a stronger foundation in math, making complex problems easier to tackle in the future.