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

If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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A train 150 m long passes a pole in 15 seconds. What is its speed?

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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 x = 3 and y = 4, what is the value of x^2 + y^2?

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What is the cube of 4?

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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If a = 2 and b = 3, what is the value of (a^2 + b^2)?

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If sin(θ) = 3/5 and θ is an acute angle, what is tan(θ)?

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If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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