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# Evaluating positive powers
- URL: https://www.esheets.io/evaluating-positive-powers/
- Published: 2025-09-11T18:06:42.000Z
- Updated: 2026-06-21T18:09:20.000Z
- Author: Richard Linnington
- Tags: Maths, Number

We often come across powers (or exponents) when dealing with things that grow or shrink quickly — like population growth, viral videos, or even computer speeds. Evaluating positive powers helps us understand how repeated multiplication works, and it's a key skill for working with scientific notation, area and volume formulas, and much more. [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise evaluating positive powers with this self-marking maths worksheet.

The interactive worksheet below generates questions, gives instant feedback, and lets students record their score.

#### What you’ll practise

- Reading the base and exponent.
- Multiplying the base by itself the correct number of times.
- Evaluating positive integer powers.
- Calculating powers accurately.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

Evaluate the following positive powers. 

## Topic guide

### What this worksheet practises

This worksheet provides practice on evaluating numbers raised to positive powers (indices). This is the fundamental building block for all higher-level algebra, standard form, and exponential growth topics.

### Key method

A power (or index) simply tells you how many times to multiply the base number by itself.

- Identify the large base number. This is the number you will be multiplying.
- Identify the small floating number (the power or index). This tells you the total number of times the base number must appear in the multiplication sum.
- Write out the full multiplication explicitly to avoid silly errors.
- Calculate the final result step-by-step.

### Worked example

**Evaluate 24 and 5³.**

Step 1: Evaluate 24.

The base is 2\. It must appear 4 times.

Write it out: 2 × 2 × 2 × 2.

Calculate in pairs: 2 × 2 = 4\. 4 × 2 = 8\. 8 × 2 = 16.

So, 24 \= 16.

Step 2: Evaluate 5³.

The base is 5\. It must appear 3 times.

Write it out: 5 × 5 × 5.

Calculate: 5 × 5 = 25\. 25 × 5 = 125.

So, 5³ = 125.

### Common mistakes to avoid

The most common and frustrating mistake is multiplying the base number by the power. For example, saying that 24 \= 8 (because 2 × 4 = 8). The power is an instruction of *how many times* to multiply the base by itself. Writing out the full sum (2 × 2 × 2 × 2) immediately prevents this mistake.

### Things to remember

Anything to the power of 1 is just the number itself (e.g. 7¹ = 7). A much stranger rule is that anything to the power of 0 is exactly 1 (e.g. 7° = 1). Memorise this rule as it appears frequently in exams to trick students.