A power is a repeated multiplication of the same number (the base) as many times as the exponent indicates, and a root is the inverse operation that finds which number, multiplied by itself, gives a stated result. For example, 2³ = 2 × 2 × 2 = 8, and the cube root of 8 is 2. Powers and roots are learned around 6th grade and the first year of secondary school (ages 11-12) and are the foundation of algebra. This guide explains what they are and how to calculate them step by step, with examples and tables.
What is a power?
A power is a short way of writing a multiplication where the same number is repeated several times. It is written with two parts: the base (the number being repeated) and the exponent (how many times it repeats), placed above and to the right of the base.
For example, in 5³ (read “five cubed” or “five to the power of three”), 5 is the base and 3 is the exponent. This means 5 × 5 × 5 = 125.
Some cases have their own name:
- Squared (exponent 2): 4² = 4 × 4 = 16.
- Cubed (exponent 3): 4³ = 4 × 4 × 4 = 64.
- To the power of 1: any number to the power of 1 is itself (7¹ = 7).
- To the power of 0: any number (except 0) to the power of 0 equals 1 (7⁰ = 1).
A very common mistake is confusing 2³ with 2 × 3: they are not the same. 2³ is 2 × 2 × 2 = 8, while 2 × 3 = 6. Before moving on, it helps to be solid on basic multiplication tables, because a power is nothing more than a repeated multiplication.
Tip: once your child understands that the exponent counts “how many times it multiplies”, they stop memorizing loose results and start reasoning through any power. Try a free class and watch them apply it with real examples.
