Topic 3
Class slides 38–44Exponents
An exponent is a shortcut for repeated multiplication. In 4³, 4 is the base and 3 is the exponent: multiply three 4s.
How to answer questions
- Find the base and the small raised number, called the exponent.
- Write the base as a factor that many times.
- Multiply to evaluate, or count repeated factors to write a power.
Worked example
4 × 4 × 4 = 4³ = 64The exponent 3 means three 4s multiplied. It does not mean 4 × 3.
How to prepare
Practise turning multiplication into powers and powers back into multiplication. Learn small squares such as 2² through 12².
Watch out: 3² = 9, while 3 × 2 = 6.
Try it:
Write 2 × 2 × 2 × 2 × 2 as a power and calculate it.
Show answer
There are five 2s, so the power is 2⁵. Its value is 32.
More practice · 3 questions
Try all three before you open the solutions.
Warm-up
Write 6 × 6 × 6 as a power, then evaluate it.
Show solution
There are three 6s, so write 6³. Then 6 × 6 × 6 = 216.
Practice
Evaluate 3⁴.
Show solution
The exponent is 4, so multiply four 3s: 3 × 3 × 3 × 3 = 81.
Challenge
Which is greater: 2⁵ or 5²? Show both values.
Show solution
2⁵ = 2 × 2 × 2 × 2 × 2 = 32. 5² = 5 × 5 = 25. Therefore 2⁵ is greater.