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Power for SQA National 5 Maths

Power

This page covers the following topics:

1. Powers
2. Multiplying powers
3. Dividing powers
4. Power to a power
5. Power of zero
6. Fractional powers

Powers are a way of representing numbers or variables that are being multiplied by themselves. The small floating number at the top of the number or variable is called its power.

Powers

To multiply powers, the multiplication rule is used. The multiplication rule states that when terms are multiplied, the powers of the terms are added together. This rule is used on all types of powers, whether they are positive, negative or fractional.

Multiplying powers

To divide powers, the division rule is used. The division rule states that when terms are divided, the powers of the terms are subtracted.

Dividing powers

To raise a power by a power, the power rule is used. The power rule states that to raise a power by a power, the two powers must be multiplied together.

Power to a power

The power of zero rule states that anything raised to the power of zero is 1.

Power of zero

When a term has a fractional power, it can be converted to a root. When the power is 1/b, the b-th root is taken. When the fractional power has a numerator other than 1, ie. c/b, the term is raised to the power of c and the b-th root is taken.

Fractional powers

1

Simplify (3wā¶)Ā² āˆ’ (wĀ³)ā“.

Using the power rule, (3wā¶)Ā² āˆ’ (wĀ³)ā“ = 9wĀ¹Ā² āˆ’ wĀ¹Ā² = 8wĀ¹Ā².

8wĀ¹Ā²

Simplify (3wā¶)Ā² āˆ’ (wĀ³)ā“.

2

Show that ā·āˆš(wāµ) and (ā·āˆšw)āµ are the same.

ā·āˆš(wāµ) = (wāµ)Ā¹Ź¹ā· = wāµŹ¹ā· and (ā·āˆšw)āµ = (wĀ¹Ź¹ā·)āµ = wāµŹ¹ā·, so the two are the same.

5 Ɨ 1/7 = 1/7 Ɨ 5

Show that ā·āˆš(wāµ) and (ā·āˆšw)āµ are the same.

3

Simplify (2sĀ²)Ā³ Ɨ (3sā“p)Ā² Ć· (2sĀ²)Ā².

Using the power rule and the multiplication rule, (2sĀ²)Ā³ Ɨ (3sā“p)Ā² Ć· (2sĀ²)Ā² = 8sā¶ Ɨ 9sāøpĀ² Ć· 4sā“ = 18sĀ¹ā°pĀ².

18sĀ¹ā°pĀ²

Simplify (2sĀ²)Ā³ Ɨ (3sā“p)Ā² Ć· (2sĀ²)Ā².

4

Calculate 8Ā¹Ź¹Ā³ Ɨ 81Ā¹Ź¹ā“.

8Ā¹Ź¹Ā³ Ɨ 81Ā¹Ź¹ā“ = Ā³āˆš8 Ɨ ā“āˆš81 = 2 Ɨ 3 = 6

6

Calculate 8Ā¹Ź¹Ā³ Ɨ 81Ā¹Ź¹ā“.

5

Calculate 32Ā²Ź¹āµ.

32Ā²Ź¹āµ = (āµāˆš32)Ā² = 2Ā² = 4

4

Calculate 32Ā²Ź¹āµ.

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