Question #6452217Fill in the Blank
Algebra-2
Question
Solve the equation . The value of is __________.
Answer & Analysis
Analysis
Question Analysis
This question involves solving an exponential equation with a square root (a radical), which requires rewriting the radical as a rational exponent.
The main focus is on converting the square root to a power of 2 and then equating exponents.
Key Concept Explanation
A square root of a number is equivalent to that number raised to the power: (where ). For higher roots, .
Combining this with the Power of a Power Rule allows us to simplify the left side of the equation.
Step-by-Step Solution
1. Rewrite the square root as a rational exponent: .
2. Apply the Power of a Power Rule: Multiply the exponents: .
3. Substitute back into the original equation: .
4. Apply the One-to-One Property: Set exponents equal:
This question involves solving an exponential equation with a square root (a radical), which requires rewriting the radical as a rational exponent.
The main focus is on converting the square root to a power of 2 and then equating exponents.
Key Concept Explanation
A square root of a number is equivalent to that number raised to the power: (where ). For higher roots, .
Combining this with the Power of a Power Rule allows us to simplify the left side of the equation.
Step-by-Step Solution
1. Rewrite the square root as a rational exponent: .
2. Apply the Power of a Power Rule: Multiply the exponents: .
3. Substitute back into the original equation: .
4. Apply the One-to-One Property: Set exponents equal:
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