Power in Maths definition
A power in maths is a compact way of writing repeated multiplication. It shows how many times a number, letter or algebraic term is multiplied by itself. The main number is called the base, and the small raised number is called the exponent, index or power. For example, 4 to the power of 3 means 4 times 4 times 4, which equals 64. The base is 4 and the exponent is 3.
Power notation is useful because repeated multiplication can become long and difficult to read. Instead of writing 2 times 2 times 2 times 2 times 2, we can write 2 to the power of 5. This means the base 2 is used as a factor five times. A common mistake is to multiply the base by the exponent. For example, 2 to the power of 5 is 32, not 10.
Powers are used in number, algebra, standard form, surds, geometry, sequences, graphs, compound interest, science and real-life modelling. At GCSE level, students work with square numbers, cube numbers, powers of 10, standard form and the laws of indices. At A-Level, powers connect to exponential functions, logarithms, calculus, binomial expansion and mathematical models of growth or decay.
Some powers have special names. A power of 2 is called a square. For example, 6 squared means 6 times 6, which equals 36. A power of 3 is called a cube. For example, 5 cubed means 5 times 5 times 5, which equals 125. These names connect powers to geometry because square numbers can represent square areas and cube numbers can represent cube volumes.
Powers also appear with algebraic terms. The expression x to the power of 4 means x times x times x times x. The expression 3x squared means 3 multiplied by x squared. Students should read expressions carefully because 3x squared is different from 3x all squared. Brackets can change the meaning of a power, so notation matters a lot in algebra.
The laws of indices are rules for simplifying powers. When multiplying powers with the same base, add the indices. When dividing powers with the same base, subtract the indices. A power raised to another power means multiply the indices. These rules help students simplify algebra quickly and accurately, especially in GCSE and A-Level questions involving expressions, standard form and functions.
Powers of 10 are especially important in standard form. Large numbers and very small numbers can be written compactly using powers of 10. For example, 3,200,000 can be written as 3.2 times 10 to the power of 6. This is useful in science, engineering, finance and calculator work because it makes very large or very small values easier to compare and calculate with.
Related ideas include base, exponent, index number, square numbers, cube numbers, standard form, surds, exponential functions and logarithms. A clear definition of power helps students understand that powers are not just small numbers written above other numbers. They describe repeated multiplication and provide a compact language for growth, scale, area, volume and advanced algebra.