This model demonstrates the laws (rules) of exponents in an interactive and visual way.
Using a rotating wheel or disc system, each rotation reveals a different law of indices with an example — helping students easily understand how powers behave in multiplication, division, and powers of powers.
Laws of Indices / Exponents:
1️⃣ Product Law:
am×an=am+na^m \times a^n = a^{m+n}am×an=am+n
2️⃣ Quotient Law:
aman=am−n\frac{a^m}{a^n} = a^{m-n}anam=am−n
3️⃣ Power of a Power:
(am)n=amn(a^m)^n = a^{mn}(am)n=amn
4️⃣ Power of a Product:
(ab)m=ambm(ab)^m = a^m b^m(ab)m=ambm
5️⃣ Power of a Quotient:
(ab)m=ambm\left(\frac{a}{b}\right)^m = \frac{a^m}{b^m}(ba)m=bmam
6️⃣ Zero Exponent Law:
a0=1a^0 = 1a0=1
7️⃣ Negative Exponent Law:
a−n=1ana^{-n} = \frac{1}{a^n}a−n=an1
Materials Required:
- Cardboard / thick chart paper
- One round plastic or cardboard disc (rotating wheel)
- A small skewer stick / straw / screw / pin for rotation
- Thermocol or small wooden base
- Sketch pens, scale, glue, tape
- Printed formulas or handmade law cards
- Colored paper for decoration
- Small LED light (optional for highlighting)
- Fevicol or glue gun
Step-by-Step Model Making:
Step 1 – Prepare the Base
- Take a strong cardboard or thermocol base (size: around 12×12 inches).
- Cover it with colored chart paper neatly.
- Write the title on top:
“Laws of Indices (Exponents) – Maths Working Model”
Step 2 – Create the Rotating Disc
- Cut a large circular wheel (8–10 inches diameter) from cardboard.
- Divide the circle into 7 equal sections (like pizza slices).
- In each section, write one law of exponents clearly along with a simple example:
Step 3 – Attach the Rotating Mechanism
- Fix a small wooden stick, skewer, or straw through the center of the disc.
- Attach it to the base so it can rotate freely.
- Optionally, use a small bottle cap or nut as a pivot at the center.
- You can also make a vertical rotating stand (wheel standing upright) using two side supports.
Step 4 – Label and Decorate
- On the base, write:
“Rotate the Wheel to Learn Each Law of Indices” - Add arrows to show rotation direction.
- Use small images or symbols (×, ÷, ^, =) for visual appeal.
- You can also place mini formula cards beside the wheel for revision.
Step 5 – Optional LED Highlight
- Add a small LED light or pointer at the top of the wheel (fixed to base).
- As the wheel rotates, the LED can point at one law at a time — making it look like an interactive “law selector.”
Explanation (for Presentation):
“This rotating model explains the Laws of Indices. When we rotate the wheel, each section displays a law — for example, when bases are the same and multiplied, we add their powers. These rules help simplify complex exponential expressions easily. This model makes algebra fun and easy to learn.”