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Exponents And Radicals — Flashcards

NIOS · Class 10 · Maths

30 flashcards for Exponents And Radicals (NIOS Class 10 Maths) to test yourself on key terms and facts. Sample: "Write 7 × 7 × 7 × 7 in exponential form"

37 questions30 flashcards14 formulas & key relations5 concepts

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A labeled diagram explaining the components of exponential notation (base, exponent, power) with examples.
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30 Flashcards·
Exponential notationPowers of rational numbersReciprocal of a powerLaws of exponents
Card 1Exponential notation

Write 7 × 7 × 7 × 7 in exponential form and name the base and exponent.

Answer

Step 1: Count how many times 7 is multiplied by itself. Step 2: 7 is multiplied 4 times, so the exponential form is 7^4. Step 3: Base = 7 and exponent = 4. Answer: 7^4, base 7, exponent 4.

Card 2Powers of rational numbers

Evaluate (2/7)^3.

Answer

Step 1: Expand the power. (2/7)^3 = (2/7) × (2/7) × (2/7) Step 2: Multiply numerators and denominators separately. = (2 × 2 × 2)/(7 × 7 × 7) Step 3: Simplify. = 8/343 Answer: 8/343.

Card 3Reciprocal of a power

Find the reciprocal of (3/5)^4 and write it in exponential form.

Answer

Step 1: Use the reciprocal rule. The reciprocal of (p/q)^m is (q/p)^m. Step 2: Reverse the fraction. Reciprocal of (3/5)^4 = (5/3)^4 Step 3: Check by expanding if needed. (3/5)^4 × (5/3)^4 = 1 Answer:…

Card 4Laws of exponents

Simplify 3^2 × 3^5.

Answer

Step 1: Use Law 1 for same bases. a^m × a^n = a^(m+n) Step 2: Add the exponents. 3^2 × 3^5 = 3^(2+5) Step 3: Simplify. = 3^7 Answer: 3^7.

Card 5Laws of exponents

Evaluate (-3/2)^3 × (-3/2)^5.

Answer

Step 1: Same base, so add exponents. (-3/2)^3 × (-3/2)^5 = (-3/2)^(3+5) Step 2: Add. = (-3/2)^8 Step 3: Evaluate the power. = 3^8 / 2^8 = 6561/256 Answer: 6561/256.

Card 6Laws of exponents

Simplify (7/4)^6 ÷ (7/4)^2.

Answer

Step 1: Same base, division means subtract exponents. (7/4)^6 ÷ (7/4)^2 = (7/4)^(6-2) Step 2: Simplify. = (7/4)^4 Step 3: Evaluate if needed. = 7^4 / 4^4 = 2401/256 Answer: 2401/256.

Card 7Laws of exponents

Simplify (3/7)^6 ÷ (3/7)^9.

Answer

Step 1: Here the denominator exponent is larger. Use Law 3: a^m ÷ a^n = 1/a^(n-m) when n > m. Step 2: Apply the rule. (3/7)^6 ÷ (3/7)^9 = 1/(3/7)^(9-6) Step 3: Simplify. = 1/(3/7)^3 = (7/3)^3 = 343/27…

Card 8Laws of exponents

Simplify [(2/5)^2]^3.

Answer

Step 1: Use the power of a power law. (a^m)^n = a^(mn) Step 2: Multiply the exponents. [(2/5)^2]^3 = (2/5)^(2×3) Step 3: Simplify. = (2/5)^6 = 64/15625 Answer: 64/15625.

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Frequently Asked Questions

What are the important topics in Exponents And Radicals for NIOS Class 10 Maths?
Key topics in Exponents And Radicals include Exponential Notation and Basic Terms, Laws of Exponents, Rational Exponents and Prime Factorisation, Surds and Their Types. Study these first, then practise questions on each for the NIOS Class 10 board exam.
How many flashcards are available for Exponents And Radicals?
There are 30 flashcards for Exponents And Radicals covering key definitions, facts and ideas. A few sample cards are shown on this page.
How should I revise Exponents And Radicals for the NIOS Class 10 board exam?
Learn the core ideas first, then work through the 37 practice questions on Exponents And Radicals. Revise definitions regularly and use flashcards for quick recall before the exam.

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Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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