Subtracting Indices

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When dividing numbers in exponent notation with the same base, we subtract the exponents.

Consider:

Text Box: a5 ÷ a2 = = = a3

This is the second law of exponents:

Example:

Simplify the following expressions, giving your answers in exponent form

Text Box: a) 43 ÷ 42 b) y8 ÷ y6 c) d) p5 ÷ p3 ÷ p

Solution:

Text Box: a) 43 ÷ 42 = 43–2 = 41 = 4 b) y8 ÷ y6 = y8–6 = y2 c) d)

Common Error : The second law of exponent does NOT apply to subtraction of numbers in exponent notation.

The following video shows more examples of subtraction of exponents:

Subtracting Exponents

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