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

The simple interest on Rs. 4000 at 5% per annum for 2 years is:

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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If the sum of three consecutive integers is 72, what are the integers?

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What is the square root of 0.25?

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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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What is the greatest common divisor (GCD) of 36 and 48?

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If a cylinder has a radius of 7 cm and height of 10 cm, what is its volume?

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What is the HCF of 72 and 120?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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If the perimeter of a square is 36 cm, what is the length of its diagonal?

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