Power Play — StepsLabs Experiment Bay

Grade 8 — Exponents, Powers & Scientific Notation

Paper Folding Simulator

A single sheet of paper starts at 0.001 cm (0.01 mm) thick. Each fold doubles the thickness. Drag the slider to experience exponential growth.

Number of Folds (n) 0

Thickness = 0.001 × 2⁰ = 0.001 cm

Calculated Thickness 0.001 cm

Real-world Comparison —

Growth Chart

In Linear Scale, thickness stays flat initially and then skyrockets vertically — demonstrating the astonishing power of exponential growth!

Milestone Presets

1. Product Rule: n^a × n^b = n^a+b

Base n =

Exp a =

Exp b =

2. Power of a Power: (n^a)^b = n^a×b

Base n =

Inner a =

Outer b =

3. Quotient Rule: n^a ÷ n^b = n^a−b

Base n =

Exp a =

Exp b =

4. Zero & Negative Exponents: n⁰ = 1 & n^−a = 1 / n^a

Base n =

Exponent e =

5. Power of a Product: m^a × n^a = (m × n)^a

m =

n =

a =

6. Power of a Quotient: (m / n)^a = m^a / n^a

m =

n =

a =

Standard Form (Scientific Notation) Converter

Standard Form is written as k × 10ⁿ, where 1 ≤ |k| < 10 and n is an integer exponent.

Convert Scientific Form back to Standard Number

Coefficient k =

× 10ⁿ where n =

Comparing Astronomical Distances (metres)

Sun → Earth

1.496 × 10¹¹ m

Sun → Saturn

1.4335 × 10¹² m

Saturn → Uranus

1.439 × 10¹² m

The exponent n represents the order of magnitude. A difference of 1 in the exponent means 10 times larger!

Powers of 10 Scale Explorer

Powers of 10 — Time Scale

Power	Time in Seconds	Real-world Event / Milestone
10⁰ s	1 s	Ball thrown up falls back to hand
10² s	~100 s (1.6 min)	Make a quick cup of tea
10⁴ s	~2.7 hours	Digest a normal meal
10⁶ s	~11.6 days	Short vacation
10⁸ s	~3.17 years	Lifespan of a hamster / mouse
10⁹ s	~31.7 years	1 billion seconds (~human middle age)
10¹¹ s	~3,170 years	Age of oldest living bristlecone pine tree
10¹⁵ s	~31.7 million years	Formation of the Himalayan mountain range
10¹⁷ s	~4.35 billion years	Age of Planet Earth (~4.54 billion yrs)

Q1. Express in Exponential Form

6 × 6 × 6 × 6 =

Q2. Prime Factorisation in Exponential Form

648 =

Q3. Simplify using Exponent Laws

2⁴ × 2⁷ =

Q4. Express in Standard Form

34,30,000 =

Q5. Negative Exponent Evaluation

5⁻² =

Q6. Magical Lotus Pond Problem

Lotuses double every day. The pond is fully covered on Day 30. On which day was it exactly half covered?

Day number =