Multiplying indices instead of adding when multiplying powers
"The Power Multiplier"
The Mistake in Action
Simplify $a^3 \times a^4$
Wrong: $a^{3 \times 4} = a^{12}$
Why It Happens
Students confuse the rules for multiplying powers with the rule for a power of a power. They multiply the indices instead of adding them.
The Fix
When multiplying powers with the same base, ADD the indices.
$$a^m \times a^n = a^{m+n}$$
$$a^3 \times a^4 = a^{3+4} = a^7$$
Think about it: $a^3$ means $a \times a \times a$, and $a^4$ means $a \times a \times a \times a$. Together that's 7 $a$'s multiplied, so $a^7$.
Memory aid: "Times means Plus" for indices (when bases are the same)
Spot the Mistake
Can you identify where this student went wrong?
Simplify $a^3 \times a^4$
$= a^{3 \times 4} = a^{12}$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: