1. What is the Power of 10 Multiplication Rule?

The power of 10 multiplication rule states that when multiplying two powers of 10 together, you can simply add their exponents. This is a fundamental property of exponents in mathematics.

2. How Does the Calculator Work?

The calculator uses the exponent addition rule:

Where:

• \( a \) — First exponent (unitless)
• \( b \) — Second exponent (unitless)
• \( a + b \) — Resulting exponent

Explanation: This rule works because multiplying exponential terms with the same base (in this case, 10) requires adding their exponents.

3. Importance of Exponent Rules

Details: Understanding exponent rules is crucial for working with scientific notation, logarithmic scales, and many areas of mathematics and science including physics, chemistry, and engineering.

4. Using the Calculator

Tips: Enter any two exponents (positive or negative, whole numbers or decimals). The calculator will show the sum of the exponents and the resulting power of 10.

5. Frequently Asked Questions (FAQ)

Q1: Does this rule work for other bases besides 10?
A: Yes, the rule \( x^a \times x^b = x^{a+b} \) works for any base x.

Q2: What if I multiply different bases?
A: The exponent addition rule only applies when the bases are the same. Different bases cannot be combined this way.

Q3: How does this relate to scientific notation?
A: Scientific notation uses powers of 10, so this rule helps when multiplying numbers in scientific notation.

Q4: What about division of powers of 10?
A: For division, you subtract exponents: \( 10^a \div 10^b = 10^{a-b} \).

Q5: Can exponents be negative in this calculation?
A: Yes, the rule works for both positive and negative exponents.