Math Problem Statement

Work out the value of 4^(1/2) ÷ 6^(-2). Give your answer as a whole number or as a fraction in its simplest form.

Solution

The problem asks us to compute the value of 412÷624^{\frac{1}{2}} \div 6^{-2}.

We will solve this step by step:

  1. Evaluate 4124^{\frac{1}{2}}:
    The exponent 12\frac{1}{2} is equivalent to taking the square root of 4. So: 412=4=24^{\frac{1}{2}} = \sqrt{4} = 2

  2. Evaluate 626^{-2}:
    The negative exponent indicates the reciprocal of 626^2. So: 62=162=1366^{-2} = \frac{1}{6^2} = \frac{1}{36}

  3. Division of powers:
    Now, divide the results: 2÷136=2×36=722 \div \frac{1}{36} = 2 \times 36 = 72

Therefore, the value of the expression is 7272.

Let me know if you would like more details on any step or have any questions!

Related Questions:

  1. How do you simplify expressions with fractional exponents?
  2. What is the rule for negative exponents?
  3. Can fractional exponents be negative? How do you handle that?
  4. What are the properties of exponents when dividing two numbers?
  5. How would the solution change if the bases were different?

Tip:

When dividing by a fraction, remember that it is the same as multiplying by its reciprocal!

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Math Problem Analysis

Mathematical Concepts

Exponents
Fractional Exponents
Negative Exponents
Division of Powers

Formulas

a^(1/2) = sqrt(a)
a^(-n) = 1/a^n
Division of fractions: a ÷ (b/c) = a × (c/b)

Theorems

Properties of Exponents

Suitable Grade Level

Grades 8-10