5 to the negative fist power plus 4 to the negative first power

To solve \( 5^{-1} + 4^{-1} \):

1. Calculate \( 5^{-1} \):
   \[
   5^{-1} = \frac{1}{5}
   \]

2. Calculate \( 4^{-1} \):
   \[
   4^{-1} = \frac{1}{4}
   \]

3. Now add the two fractions:
   \[
   \frac{1}{5} + \frac{1}{4}
   \]

To add these fractions, find a common denominator, which is 20:

\[
\frac{1}{5} = \frac{4}{20} \quad \text{and} \quad \frac{1}{4} = \frac{5}{20}
\]

Now, add them:

\[
\frac{4}{20} + \frac{5}{20} = \frac{9}{20}
\]

Thus, the final result is:

\[
5^{-1} + 4^{-1} = \frac{9}{20}
\]

If you have any questions or need further details, feel free to ask! Here are some related questions:

1. How do you calculate powers of negative exponents?
2. Can you explain how to find a common denominator?
3. What are some properties of exponents?
4. How can this concept be applied in solving equations?
5. What is the significance of fractions in mathematical operations?

**Tip:** Remember that a negative exponent indicates the reciprocal of the base raised to the positive exponent.

5 to the negative first power plus 4 to the negative first power

Discover how to calculate 5 to the negative first power plus 4 to the negative first power. This step-by-step solution covers key concepts of exponents and fraction addition, making it suitable for students in Grades 6-8.

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