Quotients of powers
This Grade 6 algebra skill from Yoshiwara Elementary Algebra covers the quotient rule for exponents: when dividing two powers with the same base, subtract the exponents. Students learn a^m divided by a^n = a^(m-n) for any nonzero base, and apply this rule to simplify algebraic expressions.
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. 2. If the larger exponent occurs in the denominator, put the power in the denominator.
In symbols: 1. $\frac{a^m}{a^n} = a^{m n}$ if $n < m$ 2. $\frac{a^m}{a^n} = \frac{1}{a^{n m}}$ if $n m$.
Common Questions
What is the quotient rule for exponents?
When dividing powers with the same base, subtract the exponents: a^m / a^n = a^(m-n), for any nonzero base a.
How do you simplify x^7 divided by x^3?
Apply the quotient rule: x^7 / x^3 = x^(7-3) = x^4.
What happens when the exponents are equal in a quotient?
If m = n, then a^m / a^n = a^0 = 1. Any nonzero number divided by itself equals 1.
What if the exponent in the denominator is larger?
You get a negative exponent: a^3 / a^7 = a^(3-7) = a^(-4) = 1/a^4.
Where is the quotient of powers rule taught?
Quotients of powers is covered in the Yoshiwara Elementary Algebra textbook for Grade 6.