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

A number is increased by 20% and then decreased by 20%. What is the net change?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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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 a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

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What is the sum of all angles in a hexagon?

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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How many diagonals does a pentagon have?

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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If x^2 - 6x + 9 = 0, what is the value of x?

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