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Business Mathematics and Basic Statistics · Class 12 Commerce

Ch 3Laws of Indices — Class 12 Business Mathematics and Basic Statistics, concept-first.

This WBCHSE Class 12 Commerce Business Mathematics and Basic Statistics chapter builds a toolkit of rules — the laws of indices (also called laws of exponents) — for simplifying expressions where a number is raised to a power, without ever expanding the power out by repeated multiplication.

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Q&A

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Concepts

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Key concepts

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Power of a Power, Product, and Quotient

(multiply the indices when raising a power to another power); and (the power distributes to every factor of a product or to both parts of a quotient). must never be confused with — the two are generally different values.

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Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

1

Meaning of an Index and the Product/Quotient Laws

This WBCHSE Class 12 Commerce Business Mathematics and Basic Statistics chapter builds a toolkit of rules — the laws of indices (also called laws of exponents) — for simplifying expressions where a nu…

2

Power of a Power, Power of a Product, and Power of a Quotient

When a power is itself raised to another power, MULTIPLY the indices:

3

Zero, Negative, and Fractional Exponents

Applying the quotient law to two different ways gives a natural definition for the zero exponent. On one hand, (any nonzero number divided by itself). On the other hand, the quotient law gives .

4

Simplifying Expressions and Solving Simple Exponential Equations

To simplify an expression involving indices, apply the laws one at a time, in a clear, deliberate order: resolve any powers-of-powers first, then combine products/quotients of the same base using the…

Exercises

+Show 4 questions4 questions
  1. Q7Simplify: $(2^{-1})^{-3}$.Free
  2. Q8Simplify: $\left(\dfrac{4}{9}\right)^{-1/2}$.Free
  3. Q9Solve for $x$: $3^{x+1} = 81$.Preview
  4. Q10Simplify $\dfrac{a^3\,b^{-2}}{a^{-1}\,b^4}$, expressing the final answer using positive indices only.Preview

More questions

+Show 6 questions6 questions
  1. Example 1Simplify: $2^3 \times 2^4$.Free
  2. Example 2Simplify: $\dfrac{5^7}{5^4}$.Free
  3. Example 3Simplify: $(3^2)^3$.Preview
  4. Example 4Evaluate: (i) $16^{1/2}$ (ii) $27^{1/3}$.Preview
  5. Example 5Evaluate: $8^{2/3}$.Preview
  6. Example 6Simplify $\dfrac{x^5\cdot x^{-2}}{x^{1/2}}$, expressing the answer with a single positive or fractional index.Preview