Applying index laws to different bases
"The Base Blunder"
The Mistake in Action
Simplify $2^3 \times 3^2$
Wrong: $6^5$ or $2^5$
Why It Happens
Students try to apply the index laws even when the bases are different. The laws only work when the base is the same.
The Fix
Index laws only work when the bases are the same.
For $2^3 \times 3^2$, the bases are different (2 and 3), so you cannot combine them using index laws.
Just calculate: $$2^3 \times 3^2 = 8 \times 9 = 72$$
You can only use $a^m \times a^n = a^{m+n}$ when both terms have the same base $a$.
Spot the Mistake
Can you identify where this student went wrong?
Simplify $2^3 \times 3^2$
$= 6^5$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: