Simplify (2u)^3. Write your answer without parentheses.
Understand the Problem
The question is asking us to simplify the expression (2u)^3. We need to apply the power rule for exponents and expand it appropriately without using parentheses in the final answer.
Answer
The simplified expression is \(8u^3\).
Answer for screen readers
The simplified expression is (8u^3).
Steps to Solve
- Apply the Power Rule for Exponents
According to the power rule, when raising a product to a power, we can raise each factor to that power:
$$(ab)^n = a^n \cdot b^n$$
For our expression $(2u)^3$, we apply it as follows:
$$(2u)^3 = 2^3 \cdot u^3$$
- Calculate the Exponent for Each Factor
Now we compute each of these exponents:
- For $2^3$, we have:
$$2^3 = 2 \cdot 2 \cdot 2 = 8$$
- For $u^3$, it simply remains as $u^3$.
- Combine the Results
Now we can put both results back together without parentheses:
$$8 \cdot u^3$$
Thus, the simplified expression is:
$$8u^3$$
The simplified expression is (8u^3).
More Information
The expression ( (2u)^3 ) illustrates how the power rule for exponents works, highlighting the importance of correctly applying the rule to both numerical coefficients and variables. This process expands to show how the base elements of the product are managed individually.
Tips
One common mistake is forgetting to apply the exponent to both parts of the product. Some may incorrectly compute ( 2^3 ) as a separate value while neglecting ( u^3 ). Always apply the exponent to all factors in the parentheses.
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