Exponents And Radicals
NIOS · Class 10 · Maths
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See them allWrite 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.
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.
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:…
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.
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.
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.
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…
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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