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OCR GCSE Maths Power

Power

This page covers the following topics:

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

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Simplify the following expression: 3 Γ— q Γ— q Γ— z Γ— z Γ— z.

OCR GCSE Maths Power Simplify the following expression: 3 Γ— q Γ— q Γ— z Γ— z Γ— z.
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2

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Write 11a⁢b³ as a product of all its factors.

OCR GCSE Maths Power Write 11a⁢b³ as a product of all its factors.
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3

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Using the multiplication rule, explain why w Γ— w Γ— w = wΒ³.

OCR GCSE Maths Power Using the multiplication rule, explain why w Γ— w Γ— w = wΒ³.
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4

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Simplify the following: 11 Γ— w⁻² Γ— w⁡ʹ².

OCR GCSE Maths Power Simplify the following: 11 Γ— w⁻² Γ— w⁡ʹ².
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5

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Given that 4 Γ— 2 Γ— 32 = 2Λ’, find s.

OCR GCSE Maths Power Given that 4 Γ— 2 Γ— 32 = 2Λ’, find s.
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6

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Give the following as a single term: 40a⁹ ÷ 5a⁡.

OCR GCSE Maths Power Give the following as a single term: 40a⁹ ÷ 5a⁡.
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7

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Given that 25 Γ— 5Λ’ = 625, find s.

OCR GCSE Maths Power Given that 25 Γ— 5Λ’ = 625, find s.
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8

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The volume of the given cuboid is 45k²⁰. Calculate the unknown side.

OCR GCSE Maths Power The volume of the given cuboid is 45k²⁰. Calculate the unknown side.
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9

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Simplify (3w⁢)Β² βˆ’ (wΒ³)⁴.

OCR GCSE Maths Power Simplify (3w⁢)Β² βˆ’ (wΒ³)⁴.
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10

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Simplify (2sΒ²)Β³ Γ— (3s⁴p)Β² Γ· (2sΒ²)Β².

OCR GCSE Maths Power Simplify (2sΒ²)Β³ Γ— (3s⁴p)Β² Γ· (2sΒ²)Β².
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11

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Simplify 5x⁰.

OCR GCSE Maths Power Simplify 5x⁰.
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12

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Simplify 12wΒ³/6wwΒ².

OCR GCSE Maths Power Simplify 12wΒ³/6wwΒ².
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13

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Simplify (2q³)²/4qq⁡.

OCR GCSE Maths Power Simplify (2q³)²/4qq⁡.
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14

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Calculate 32²ʹ⁡.

OCR GCSE Maths Power Calculate 32²ʹ⁡.
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15

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Simplify x⁸ Γ— (1/16)⁰ Γ— 49ΒΉΚΉΒ².

OCR GCSE Maths Power Simplify x⁸ Γ— (1/16)⁰ Γ— 49ΒΉΚΉΒ².
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16

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Find the area of the given rectangle.

OCR GCSE Maths Power Find the area of the given rectangle.
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