Rules or Laws of Indices
Video lessons with examples and solutions to help GCSE Maths students
learn about the rules or laws of indices.
What are the Law of Indices?
\[\begin{array}{l}{x^0} = 1\\{x^m} \times {x^n} = {x^{m + n}}\\\frac{{{x^m}}}{{{x^n}}} = {x^{m - n}}\\{\left( {{x^m}} \right)^n} = {x^{mn}}\\{x^{ - m}} = \frac{1}{{{x^m}}}\\{x^{\frac{m}{n}}} = \sqrt[n]{{{x^m}}} = {\left( {\sqrt[n]{x}} \right)^m}\end{array}\]
GCSE Maths - Rules of Indices (1) (Multiplication and Division)
GCSE Maths - Rules of Indices (2) (Raising to a Power and Zero Power)
GCSE Maths - Rules of Indices (3) (Negative and Fractional Powers)
Index Laws - Ultimate revision guide for Further maths GCSE
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
\[\begin{array}{l}{x^0} = 1\\{x^m} \times {x^n} = {x^{m + n}}\\\frac{{{x^m}}}{{{x^n}}} = {x^{m - n}}\\{\left( {{x^m}} \right)^n} = {x^{mn}}\\{x^{ - m}} = \frac{1}{{{x^m}}}\\{x^{\frac{m}{n}}} = \sqrt[n]{{{x^m}}} = {\left( {\sqrt[n]{x}} \right)^m}\end{array}\]
GCSE Maths - Rules of Indices (1) (Multiplication and Division)
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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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