Second law of exponents
The Second Law of Exponents explains how to divide two powers with the same base by subtracting the smaller exponent from the larger, a key rule covered in Yoshiwara Elementary Algebra Chapter 7: Polynomials. For Grade 6 students, this law simplifies expressions like a^m ÷ a^n = a^(m-n) when m > n, or 1/a^(n-m) when n > m. Understanding this rule is essential for simplifying polynomial and rational expressions in algebra.
Key Concepts
Property To divide two powers with the same base, we subtract the smaller exponent from the larger one, and keep the same base.
1. If the larger exponent occurs in the numerator, put the power in the numerator.
$$\frac{a^m}{a^n} = a^{m n} \text{ if } n < m$$.
Common Questions
What is the second law of exponents?
The second law states that when dividing powers with the same base, you subtract exponents: a^m ÷ a^n = a^(m-n) if m > n, or 1/a^(n-m) if n > m.
How do you divide powers with the same base?
Keep the base the same and subtract the smaller exponent from the larger. If the larger exponent is in the numerator, the result stays positive; if it is in the denominator, the result is a fraction.
Where is the second law of exponents in Yoshiwara Elementary Algebra?
It is covered in Chapter 7: Polynomials of Yoshiwara Elementary Algebra, alongside other exponent rules used for simplifying polynomial expressions.
What is the difference between the first and second laws of exponents?
The first law covers multiplication (add exponents), while the second law covers division (subtract exponents) of powers with the same base.
Why do we subtract exponents when dividing?
Because division cancels matching factors. For example, a^5 ÷ a^3 means five a-factors divided by three a-factors, leaving two a-factors, so the result is a^2.