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[PDF] 42 – Working with Integer Exponents

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[PDF] 42 – Working with Integer Exponents

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4.2 ² Working with Integer Exponents

Multiplying Exponential Numbers

To multiply powers with the same base, keep the base the same and add the exponents. For example, 35 × 33 = 38. If the bases are not the same, calculate each power separately and then multiply.

Example One

Simplify the following expressions where possible.

43 × 42 74 × 53 28 × 2-3

x5 × x-1 a-3 × a5x b4x-1 × b13 + 2x

Dividing Exponential Numbers

To divide powers with the same base, keep the base the same and subtract the exponents. For example 57 ÷ 53 = 54. If the bases are not the same, calculate each power separately and then divide.

Example Two

Simplify the following expressions where possible.

44 ÷ 41 26 ÷ 23 x5 ÷ y2

92 ÷ 96 x5 ÷ x8 4x ÷ 46

The Power of a Power

The power of a power means that an exponential number is being raised to an exponent. When this is the case, the two exponents are multiplied together and the base remains the same.

For example, (23)4 = 212.

Example Three

Simplify the following expressions where possible. (25)3 (34)6 (x-2)3 (49)x (5x + 2)3 ((-2)7)2

Negative Exponents

A term raised to a negative exponent is equivalent to the reciprocal of that term, being raised to the positive of that exponent.

For example, 7-2 = ଵ

;మ and ଵ 6ష/ = 23.

Example Four

Rewrite the following expressions with positive exponents.

5-1 2-4 x-3

3-x (ଶ

7)-4 (ହ 8)-2

Zero Exponents

Any base (except for 0) raised to the exponent of zero is equal to 1.

For example, 30 = 1 a0 = 1 (ξ

;)0 = 1

Example Five

Simplify the following expressions. Leave your answer as an exponential number with a positive exponent. ଷఱ

H7ష.

ሺ:7ష/ሻమሻ (23)2 ÷ 211 Complete: p. 221 - 223#1, 2ace, 4 ² 6ace, 13ade.