Exponents And Radicals
NIOS · Class 10 · Maths
Flashcards for Exponents And Radicals — NIOS Class 10 Maths. Quick Q&A cards covering key concepts, definitions, and formulas.
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See them allEvaluate: (3/4)³
Answer
Step 1: Apply exponent to numerator and denominator separately → (3³)/(4³) Step 2: Calculate 3³ = 3 × 3 × 3 = 27 Step 3: Calculate 4³ = 4 × 4 × 4 = 64 Step 4: Write final answer → 27/64 Answer: 27/64…
Simplify: 5² × 5³
Answer
Step 1: Apply Law 1 - aᵐ × aⁿ = aᵐ⁺ⁿ Step 2: Add the exponents → 5²⁺³ = 5⁵ Step 3: Calculate 5⁵ = 5 × 5 × 5 × 5 × 5 = 3125 Answer: 5⁵ = 3125 Formula Used: aᵐ × aⁿ = aᵐ⁺ⁿ…
Find the value of (-2/3)⁻²
Answer
Step 1: Apply negative exponent rule → a⁻ⁿ = 1/aⁿ Step 2: Write as positive exponent → 1/(-2/3)² Step 3: Calculate (-2/3)² = (-2)²/(3)² = 4/9 Step 4: Take reciprocal → 1 ÷ (4/9) = 9/4 Answer: 9/4 Key …
Express 72 as a product of prime powers
Answer
Step 1: Divide by smallest prime → 72 ÷ 2 = 36 Step 2: Continue division → 36 ÷ 2 = 18, 18 ÷ 2 = 9 Step 3: 9 ÷ 3 = 3, 3 ÷ 3 = 1 Step 4: Count prime factors → 2 appears 3 times, 3 appears 2 times Answe…
Simplify: (2³)⁴
Answer
Step 1: Apply power rule → (aᵐ)ⁿ = aᵐⁿ Step 2: Multiply exponents → 2³ˣ⁴ = 2¹² Step 3: Calculate 2¹² = 2¹⁰ × 2² = 1024 × 4 = 4096 Answer: 2¹² = 4096 Formula Used: (aᵐ)ⁿ = aᵐⁿ…
Calculate: (625)^(1/4)
Answer
Step 1: Find prime factorization → 625 = 5⁴ Step 2: Apply fractional exponent → (5⁴)^(1/4) Step 3: Use power rule → 5^(4×1/4) = 5¹ Step 4: Simplify → 5¹ = 5 Answer: 5 Key Concept: a^(1/n) = ⁿ√a (nth r…
Which of these are surds: √49, √50, ∛64, √(2+√3)?
Answer
Step 1: Check √49 → √49 = 7 (rational) → NOT a surd Step 2: Check √50 → √50 = 5√2 (irrational) → IS a surd Step 3: Check ∛64 → ∛64 = 4 (rational) → NOT a surd Step 4: Check √(2+√3) → Root of irrationa…
Express √72 in simplest form
Answer
Step 1: Find prime factorization → 72 = 2³ × 3² = 8 × 9 Step 2: Group perfect squares → 72 = 4 × 2 × 9 = 36 × 2 Step 3: Take out perfect square → √72 = √(36 × 2) = √36 × √2 Step 4: Simplify → 6√2 Answ…
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