Math Problem Statement

Evaluate the expression: 2(4^{-1/2}) - 2^0 + 2^{3/2} + 2^2

Solution

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The expression appears to be:

2(412)20+232+222 \left( 4^{-\frac{1}{2}} \right) - 2^0 + 2^{\frac{3}{2}} + 2^2

Let's solve this step by step.

  1. 412=14=124^{-\frac{1}{2}} = \frac{1}{\sqrt{4}} = \frac{1}{2}
  2. 2×12=12 \times \frac{1}{2} = 1
  3. 20=12^0 = 1
  4. 232=23=82.8282^{\frac{3}{2}} = \sqrt{2^3} = \sqrt{8} \approx 2.828
  5. 22=42^2 = 4

Now, the full expression becomes: 11+2.828+41 - 1 + 2.828 + 4

Let's compute the final result.The result of the expression:

2(412)20+232+222 \left( 4^{-\frac{1}{2}} \right) - 2^0 + 2^{\frac{3}{2}} + 2^2

is approximately 6.8286.828.

Would you like further details or explanations on any step?

Here are five related questions you might find useful:

  1. What are negative exponents and how do they work?
  2. How do fractional exponents relate to roots?
  3. Why does 20=12^0 = 1?
  4. How can you simplify expressions with exponents?
  5. How does one calculate square roots of non-perfect squares?

Tip: When solving exponent expressions, handle the powers one by one to avoid confusion, especially when dealing with fractions and negatives.

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Math Problem Analysis

Mathematical Concepts

Exponents
Roots
Order of Operations

Formulas

a^m * a^n = a^{m+n}
a^0 = 1
a^{-n} = 1/a^n
Square root: \sqrt{a} = a^{1/2}

Theorems

Exponentiation Rules

Suitable Grade Level

Grades 9-10