First law of exponents
This Grade 6 algebra skill from Yoshiwara Elementary Algebra introduces the first law of exponents (product rule): when multiplying two powers with the same base, keep the base and add the exponents (a^m × a^n = a^(m+n)). This is the foundational exponent law for all algebraic manipulation involving powers.
Key Concepts
Property To multiply two powers with the same base, we add the exponents and leave the base unchanged. In symbols,.
$$a^m \cdot a^n = a^{m+n}$$.
Examples To multiply two powers with the same base, add their exponents: $x^5 \cdot x^3 = x^{5+3} = x^8$.
Common Questions
What is the first law of exponents?
The first law states that when you multiply powers with the same base, you add the exponents: a^m × a^n = a^(m+n).
Why do you add exponents when multiplying powers?
Because a^m means a multiplied m times and a^n means a multiplied n times. Multiplying them together gives a multiplied m+n times total.
What is an example using the first law of exponents?
x^4 × x^3 = x^(4+3) = x^7, because 4 factors of x times 3 factors of x gives 7 factors of x.
Does the first law apply when the bases are different?
No. You can only add exponents when the bases are identical. For example, x^2 × y^3 cannot be simplified using this law.
Where is the first law of exponents taught?
The first law of exponents is introduced in the Yoshiwara Elementary Algebra textbook for Grade 6.