Math Problem Statement
\frac{2^{-2}+2^{-3}}{4^{-2}+8^{-1}}
Solution
To simplify the expression:
we need to rewrite the terms with negative exponents as positive exponents.
Step 1: Rewrite with Positive Exponents
- (since , )
Substitute these into the original expression:
Step 2: Simplify the Numerator and Denominator
To add fractions, we need a common denominator:
- Numerator:
- Denominator:
Step 3: Divide the Fractions
Now we have:
To divide fractions, multiply by the reciprocal:
Final Answer
Would you like a breakdown of each step or have any questions?
Here are 5 related questions to consider:
- How do you simplify expressions with negative exponents?
- What are the properties of exponents when multiplying or dividing powers with the same base?
- How do you convert between different bases, such as converting and to powers of ?
- What are the rules for adding and subtracting fractions?
- How do you simplify complex fractions by multiplying by the reciprocal?
Tip: Always remember to convert negative exponents into positive exponents to make simplification easier.
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Math Problem Analysis
Mathematical Concepts
Algebra
Exponents
Fractions
Formulas
a^{-n} = \frac{1}{a^n}
\frac{a}{b} \div \frac{c}{d} = \frac{a \times d}{b \times c}
Adding fractions: \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}
Theorems
Properties of exponents
Fraction division using reciprocals
Suitable Grade Level
Grades 8-10
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