Topic Details (Notes format)

How to Work with Exponents (Laws of Exponents)

Subject: Mathematics

Book: Maths Mastery

Exponents, or powers, indicate repeated multiplication of a base number. Key laws include Product of Powers (a^m × a^n = a^(m+n)) and Power of a Power ((a^m)^n = a^(m×n)). For example, 2² × 2³ = 2^(2+3) = 2^5 = 32. Negative exponents a^–n represent 1/(a^n). Mastering exponents is vital in scientific notation, compound interest, and growth/decay problems. By consistently applying exponent laws, you can simplify expressions, solve exponential equations, and interpret phenomena like population growth or radioactive decay with ease.

Practice Questions

What is the cube of 4?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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If two complementary angles differ by 30°, what are the angles?

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If a square has a perimeter of 64 cm, what is its area?

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What is the slope of a line passing through the points (2, 3) and (4, 7)?

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The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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If a = 4 and b = 5, what is the value of (a+b)^2?

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What is the probability of drawing an ace from a standard deck of 52 cards?

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A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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