%5E1%2F2-simplified.jpeg "(25x^6)^1/2 Simplified")
Simplifying (25x^6)^1/2
This expression represents the square root of (25x^6). Let's break down the simplification process:
Understanding Exponents and Roots
- Exponents: An exponent indicates how many times a base number is multiplied by itself. In our case, x^6 means x multiplied by itself six times.
- Roots: A root is the inverse operation of an exponent. A square root asks: "What number multiplied by itself equals the given number?"
Applying the Rules
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Distribute the exponent: Since the exponent is outside the parentheses, it applies to both the coefficient (25) and the variable (x^6).
(25x^6)^1/2 = 25^1/2 * (x^6)^1/2
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Simplify the coefficient: The square root of 25 is 5.
5 * (x^6)^1/2
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Simplify the variable: When raising a power to another power, we multiply the exponents.
5 * x^(6 * 1/2) = 5 * x^3
Final Answer
Therefore, the simplified form of (25x^6)^1/2 is 5x^3.