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Laws of Indices or Powers © Christine Crisp

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Laws of Indices Generalizing this, we get: Multiplying with Indices e.g.1 e.g.2

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Laws of Indices e.g.3 Multiplying with Indices

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Laws of Indices Generalizing this, we get: Dividing with Indices Cancel e.g.

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Laws of Indices Powers of Powers e.g.by rule (1)

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Laws of Indices Powers of Powers e.g. by rule (1)

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Laws of Indices Exercises Without using a calculator, use the laws of indices to express each of the following as an integer 1. 2. 3.

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Laws of Indices A Special Case e.g. Simplify Using rule (3) Also,

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Laws of Indices e.g. Simplify Also, Using rule ( 2 ) So, Generalizing this, we get: A Special Case

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Laws of Indices Another Special Case e.g. Simplify Using rule (3) Also,

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Laws of Indices e.g. Simplify Using rule (3) Also, So, Another Special Case

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Laws of Indices Generalizing this, we get: e.g. 1 e.g. 2 Another Special Case

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Laws of Indices Fractional Powers i.e. the 4

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Laws of Indices The definition of a rational index is that p is the power q is the root e.g.1 e.g.2 e.g.3 Rational Numbers

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Laws of Indices SUMMARY The following are the laws of indices:

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Laws of Indices Exercises Without using a calculator, use the laws of indices to express each of the following as an integer 1. 2. 3.

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Laws of Indices Exercises Without using a calculator, use the laws of indices to express each of the following as an integer or fraction 4. 5. 6.

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Laws of Indices

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Review: Laws of Exponents Questions Q: 4 0 =? A: 1 Q: 4 1 =? A: 4 Q: 4 1/2 =? A: Let’s square the number (4 1/2 ) 2 =? (4 1/2 ) 2 = 4 1 = 4 Recall: b.

Review: Laws of Exponents Questions Q: 4 0 =? A: 1 Q: 4 1 =? A: 4 Q: 4 1/2 =? A: Let’s square the number (4 1/2 ) 2 =? (4 1/2 ) 2 = 4 1 = 4 Recall: b.

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