Multiply and Divide Powers Calculator

Power Rules:

\[ 10^a \times 10^b = 10^{a+b} \] \[ \frac{10^a}{10^b} = 10^{a-b} \]

Result:

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1. What Are Power Rules?

The power rules describe how to multiply and divide numbers with the same base raised to different exponents. These fundamental mathematical operations are essential in scientific calculations and exponential growth/decay problems.

2. How Does the Calculator Work?

The calculator applies these power rules:

\[ 10^a \times 10^b = 10^{a+b} \] \[ \frac{10^a}{10^b} = 10^{a-b} \]

Where:

\( a \) — First exponent (integer)
\( b \) — Second exponent (integer)
10 — Common base (can be any positive number)

Explanation: When multiplying powers with the same base, add the exponents. When dividing, subtract the exponents.

3. Importance of Power Calculations

Details: These calculations are fundamental in scientific notation, logarithmic scales (like pH and decibels), and many areas of physics and engineering.

4. Using the Calculator

Tips: Enter integer exponents (a and b), select the operation (multiply or divide), and the calculator will show the simplified result.

5. Frequently Asked Questions (FAQ)

Q1: Can this be used with bases other than 10?
A: Yes, the same rules apply to any positive base (e.g., 2, e, 5).

Q2: What if the exponents are not integers?
A: The rules still apply for fractional or decimal exponents.

Q3: How does this relate to scientific notation?
A: Scientific notation uses powers of 10, making these operations essential for working with very large or small numbers.

Q4: What about negative exponents?
A: Negative exponents represent reciprocals (10^{-a} = 1/10^a), and the same rules apply.

Q5: Can I multiply different bases?
A: No, these rules only apply when the bases are identical. Different bases require different approaches.