Powers and roots

Powers and Roots

Understanding Powers

• Powers represent the number of times a number is multiplied by itself.
• A number with a power is composed of a base and an exponent. For example, in 2³, 2 is the base and 3 is the exponent.
• Products of powers can be simplified by adding the exponents if the bases are the same. For example, 2³ * 2² = 2⁵.
• Powers to powers can be simplified by multiplying the exponents. For example, (2³)² = 2⁶.

Rules of Exponents

• Any number (except zero) raised to the power of zero equals one. For example, a⁰ = 1.
• Any number raised to the power of one equals the number itself. For example, a¹ = a.
• Negative exponents indicate the reciprocal of the number. For example, a⁻¹ = 1/a.
• Fractional exponents indicate roots. For example, a^(1/2) is equal to the square root of a, and a^(1/3) to the cube root of a.

Understanding Roots

• A root specifies the number of times a given number must be multiplied by itself to obtain the original number.
• The square root is most common and it undoes the power of 2; For example, the √4 is 2.
• Likewise, a cube root undoes the power of 3; For example, the cube root of 8 is 2.

Solving Problems Involving Powers and Roots

• Understand the problem and what the problem is asking for.
• If the problem involves powers, apply the correct rules of exponents.
• If it’s a root problem, apply the correct square, cube or other root based on the question.
• Always check solutions to ensure they meet the conditions of the problem.

This revision content provides an overview of the key concepts on powers and roots for your review. As you go through the material remember practice is the key to perfect understanding and success in the higher level of mathematics.