SEBA Class 10 Maths Revision 3 Solutions – Complete Exam Preparation Guide

Q1. Find the value of:
(i) \(11^3\)    (ii) \(2 \times 10^4\)    (iii) \(\left(\frac{1}{2}\right)^5\)    (iv) \((-4)^2\)
Answer:
We will use laws of exponents to evaluate each expression.

(i) \(11^3 = 11 \times 11 \times 11 = 1331\)
(ii) \(2 \times 10^4 = 2 \times 10000 = 20000\)
(iii) \(\left(\frac{1}{2}\right)^5 = \frac{1}{32}\)
(iv) \((-4)^2 = 16\)

Final Answer:
(i) 1331    (ii) 20000    (iii) \( \frac{1}{32} \)    (iv) 16

Q2. Express the following numbers in terms of powers of their prime factors:
(i) 720    (ii) 3125    (iii) 3600    (iv) 108 × 192
Answer:
(i) \(720 = 2^4 \times 3^2 \times 5\)
(ii) \(3125 = 5^5\)
(iii) \(3600 = 2^4 \times 3^2 \times 5^2\)
(iv) \(108 \times 192 = (2^2 \times 3^3)(2^6 \times 3) = 2^8 \times 3^4\)

Final Answer:
(i) \(2^4 \times 3^2 \times 5\)
(ii) \(5^5\)
(iii) \(2^4 \times 3^2 \times 5^2\)
(iv) \(2^8 \times 3^4\)

Q3. Simplify:
(i) \((-3)^4 \times (-5)^2\)    (ii) \((2^2 \times 2)^3\)    (iii) \(2^3 \times 3^2 \times 4^0\)    (iv) \(\left(\frac{5}{8}\right)^2 \times \left(\frac{8}{5}\right)^2\)
Answer:
(i) \((-3)^4 = 81,\; (-5)^2 = 25\)
\(81 \times 25 = 2025\)

(ii) \((2^2 \times 2)^3 = (2^3)^3 = 2^9 = 512\)

(iii) \(4^0 = 1\)
\(2^3 \times 3^2 \times 1 = 8 \times 9 = 72\)

(iv) \(\left(\frac{5}{8} \times \frac{8}{5}\right)^2 = 1^2 = 1\)

Final Answer:
(i) 2025    (ii) 512    (iii) 72    (iv) 1

Q4. Compare the following numbers:
(i) \(2^8\) and \(8^2\)    (ii) \(2.7 \times 10^5\) and \(1.5 \times 10^6\)
Answer:
(i) \(2^8 = 256,\; 8^2 = 64\)
So, \(2^8 > 8^2\)

(ii) \(2.7 \times 10^5 = 270000\)
\(1.5 \times 10^6 = 1500000\)
So, \(2.7 \times 10^5 < 1.5 \times 10^6\)

Final Answer:
(i) \(2^8 > 8^2\)
(ii) \(2.7 \times 10^5 < 1.5 \times 10^6\)

Q5. Express the following with the help of positive power:
(i) \(2^{-3} \times (-7)^{-3}\)    (ii) \((-3)^{-4} \times \left(\frac{5}{3}\right)^4\)
Answer:
(i) \(2^{-3} = \frac{1}{2^3},\; (-7)^{-3} = \frac{1}{(-7)^3}\)
\[ = \frac{1}{2^3 \times (-7)^3} \]

(ii) \((-3)^{-4} = \frac{1}{(-3)^4}\)
\[ = \frac{(5/3)^4}{3^4} = \left(\frac{5}{9}\right)^4 \]

Final Answer:
(i) \( \frac{1}{2^3 \times (-7)^3} \)
(ii) \( \left(\frac{5}{9}\right)^4 \)

Q6. Express the following numbers in standard form:
(i) 3430.000    (ii) 70,40,000,000    (iii) 0.000000015    (iv) 0.00001436
Answer:
(i) \(3.43 \times 10^3\)
(ii) \(7.04 \times 10^9\)
(iii) \(1.5 \times 10^{-8}\)
(iv) \(1.436 \times 10^{-5}\)

Final Answer:
(i) \(3.43 \times 10^3\)
(ii) \(7.04 \times 10^9\)
(iii) \(1.5 \times 10^{-8}\)
(iv) \(1.436 \times 10^{-5}\)

Q7. Express the following in general form:
(i) \(1.0001 \times 10^9\)    (ii) \(3.02 \times 10^6\)
Answer:
(i) \(1.0001 \times 10^9 = 1000100000\)
(ii) \(3.02 \times 10^6 = 3020000\)

Final Answer:
(i) 1000100000
(ii) 3020000

Q8. Find the value of m such that \( (-3)^m \times (-3)^5 = (-3)^7 \)
Answer:
Using law: \(a^m \times a^n = a^{m+n}\)

\[ (-3)^{m+5} = (-3)^7 \]
So, \(m + 5 = 7\)
\(m = 2\)

Final Answer:
\(m = 2\)

Q9. (a) The value of \(3^{-3}\) is:

(i) 3
(ii) \( \frac{1}{3} \)
(iii) \( \frac{1}{27} \)
(iv) 3×3

Answer: (iii) \( \frac{1}{27} \)

Q9. (b) The value of \( \left(\frac{2}{3}\right)^2 \) is:

(i) \( \frac{1}{(2×3)^2} \)
(ii) \( (2×3)^2 \)
(iii) \( \left(\frac{3}{2}\right)^2 \)
(iv) \( \left(\frac{2}{3}\right)^2 \)

Answer: (iv) \( \left(\frac{2}{3}\right)^2 \)

(c) The value of \( \left(-\frac{2}{3}\right)^4 \) is:

(i) \( \frac{8}{12} \)
(ii) \( \frac{16}{81} \)
(iii) \( -\frac{16}{81} \)
(iv) \( \frac{8}{12} \)

Answer: (ii) \( \frac{16}{81} \)

(d) The standard form of 0.000064 is:

(i) \(64 \times 10^4\)
(ii) \(64 \times 10^{-4}\)
(iii) \(6.4 \times 10^5\)
(iv) \(6.4 \times 10^{-5}\)

Answer: (iv) \(6.4 \times 10^{-5}\)

(e) The value of \(2.03 \times 10^{-3}\) is:

(i) 0.203
(ii) 0.000203
(iii) 203000
(iv) 0.00203

Answer: (iv) 0.00203