(√5)⁴
Understand the Problem
The question is asking to simplify or evaluate the expression (√5)⁴, which involves applying the rules for exponents and square roots.
Answer
The expression $(\sqrt{5})^4$ simplifies to $25$.
Answer for screen readers
The simplified result of $(\sqrt{5})^4$ is $25$.
Steps to Solve
- Apply the power of a power rule
When raising a power to another power, you multiply the exponents. Here, we have:
$$(\sqrt{5})^4 = (5^{1/2})^4$$
Now multiply the exponents:
$$ = 5^{(1/2) \cdot 4} = 5^{2}$$
- Simplify the expression
Now simplify $5^2$:
$$ 5^2 = 25 $$
The simplified result of $(\sqrt{5})^4$ is $25$.
More Information
This problem demonstrates the property of exponents, specifically the power of a power rule. Understanding how to manipulate roots and exponents is fundamental when dealing with expressions in algebra.
Tips
- A common mistake is forgetting to multiply the exponents correctly when using the power of a power rule. Always ensure that you properly apply the multiplication of exponents.
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