Products of powers
This Grade 6 algebra skill from Yoshiwara Elementary Algebra covers the product rule for exponents (powers of powers). Students learn that when multiplying expressions with the same base, exponents are added: a^m × a^n = a^(m+n). They also learn to simplify expressions involving products of 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 simplify $z^4 \cdot z^5$, we keep the base $z$ and add the exponents: $z^{4+5} = z^9$.
Common Questions
What is the product of powers rule?
When multiplying two expressions with the same base, keep the base and add the exponents: a^m × a^n = a^(m+n).
How do you simplify x^3 × x^5?
Keep the base x and add the exponents: x^3 × x^5 = x^(3+5) = x^8.
Does the product rule apply to different bases?
No. The product rule for exponents only applies when the bases are the same. You cannot combine 2^3 × 3^2 using this rule.
What is a common mistake with products of powers?
A common mistake is multiplying the exponents instead of adding them. For multiplication, always add exponents (not multiply).
Where are products of powers taught?
Products of powers is covered in the Yoshiwara Elementary Algebra textbook for Grade 6 students.