1.4

Powers and roots

9 flashcards to master Powers and roots

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Key Concept Flip

What is the value of 5⁰?

Answer Flip

Any non-zero number raised to the power of 0 is equal to 1. Therefore, 5⁰ = 1.

Key Concept Flip

Simplify: x⁵ × x²

Answer Flip

When multiplying indices with the same base, add the powers. x⁵ × x² = x⁵⁺² = x⁷

Key Concept Flip

Simplify: y⁸ / y³

Answer Flip

When dividing indices with the same base, subtract the powers. y⁸ / y³ = y⁸⁻³ = y⁵

Key Concept Flip

What does a negative index mean? Give an example.

Answer Flip

A negative index indicates a reciprocal.

Example: x⁻² = 1/x². Therefore, 2⁻³ = 1/2³ = 1/8
Key Concept Flip

What is the value of 9¹/²?

Answer Flip

A fractional index of 1/2 represents the square root. Therefore, 9¹/² = √9 = 3.

Key Concept Flip

Express 0.000047 in standard form (scientific notation).

Answer Flip

Standard form is A x 10ⁿ, where 1 ≤ A < 10 and n is an integer. 0.000047 = 4.7 x 10⁻⁵

Key Concept Flip

Simplify: (a³)⁴

Answer Flip

When raising a power to another power, multiply the powers. (a³)⁴ = a³ˣ⁴ = a¹²

Definition Flip

Define 'index' (or 'exponent').

Answer Flip

An index (or exponent) indicates how many times a base number is multiplied by itself.

Example: in 2³, 3 is the index, and 2 is the base. 2³ means 2 x 2 x 2.
Key Concept Flip

What is the cube root of 64?

Answer Flip

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. The cube root of 64 is 4, because 4 x 4 x 4 = 64.

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1.3 Operations and order of operations 1.5 Ratio, proportion and rate

Key Questions: Powers and roots

Define 'index' (or 'exponent').

An index (or exponent) indicates how many times a base number is multiplied by itself.

Example: in 2³, 3 is the index, and 2 is the base. 2³ means 2 x 2 x 2.

About Powers and roots (1.4)

These 9 flashcards cover everything you need to know about Powers and roots for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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