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 .
We will solve this step by step:
-
Evaluate :
The exponent is equivalent to taking the square root of 4. So: -
Evaluate :
The negative exponent indicates the reciprocal of . So: -
Division of powers:
Now, divide the results:
Therefore, the value of the expression is .
Let me know if you would like more details on any step or have any questions!
Related Questions:
- How do you simplify expressions with fractional exponents?
- What is the rule for negative exponents?
- Can fractional exponents be negative? How do you handle that?
- What are the properties of exponents when dividing two numbers?
- 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