Exponents and Powers Class 7 Worksheet

EXPONENTS AND POWERS

SECTION A – MCQs

1. Value of (3^{-2})^{-1}
a) 1/9                   b) 9                    c) 3                    d) 1/3

2. Reciprocal of 4^{-3}
a) 4^{3}                    b) 4^{-3}                    c) 1/64                    d) 64

3. (-5)^{3}
a) 125                    b) –125                    c) –25                    d) 25

4. 10^m \times 10^n = ?
a) 10^{m-n}
b) 10^{m+n}
c) 10^{mn}
d) 10^{m+n+1}

5. 2^4 \div 2^6
a) 2²                    b) 2⁻²                    c) 4                    d) 2

6. (7^{-1})^{2}
a) 7⁻²                    b) 7²                    c) 1/7                    d) 1/49

7. Standard form of 0.00000092
a) 9.2 \times 10^6
b) 9.2 \times 10^{-7}
c) 92 \times 10^{-6}
d) 9.2 \times 10^{-5}

8.
(-1)^{57}
a) 0                    b) –1                    c) 1                    d) 57

9. Correct law:
a) a^m + a^m = a^{2m}
b) a^m \times a^n = a^{m+n}
c) a^m \div a^n = a^{m+n}
d) a^m \times a^n = a^{m-n}

10.
(0.1)^{-2}
a) 0.01                    b) 0.1                    c) 10                    d) 100

SECTION B – VERY SHORT ANSWERS

11. Express in standard form:

a) 0.000057
b) 3,940,000

12. Express in usual form:

a) 4.5 \times 10^{3}
b) 7.2 \times 10^{-4}

13. Evaluate:  5^{-1} + 2^{-1}

14. If:  2^{m} \times 2^{5} = 2^{10}

Find m.

15. Simplify:

(8^{3} \div 8^{2})^{-1}

16. Write in exponential form:

3 \times 3 \times 3 \times 3^{2}

17. Find:

(−2)^{4}

18. Simplify:

9^{-1} - 3^{-2}

19. Solve for x:

10^{x} = 0.001

20. Write reciprocal form of:

6^{-3}

SECTION C – SHORT ANSWER QUESTIONS (6 Questions)

21. Simplify:

(11^{7} \div 11^{3})^{2} \times 11^{-5}

22. Convert to standard form and add:

4.2 \times 10^{5}, \quad 9.5 \times 10^{4}

23. Simplify:

\frac{2^{-3} \times 4^{2}}{8^{-1}}

24. Evaluate:

(7^{-2} - 5^{-2})^{-1}

25. Write as a single power of 5:

5^{4} \times 5^{-7} \times 5^{3}

26. Find a:

(3^{4} \div 3^{2}) \times 3^{a} = 3^{8}

SECTION D – LONG ANSWER QUESTIONS

27. Simplify completely:
\frac{16^{-2} \times 8^{-1} \times 2^{5}}{4^{-3}}

28. Jupiter mass:

1.90 \times 10^{27} \text{ kg}
Sun mass:
1.989 \times 10^{30} \text{ kg}

Find:
a) Total mass
b) How many times heavier the Sun is

29. Find x:

\frac{(-6)^{-5}}{x} = (-6)^{-2}

30. Solve for x:

a) 3^{x+1} = 81
b) 2^{,x-2} \times 2^{3} = 64

ANSWER SHEET


SECTION A – MCQs

1 – b
2 – a
3 – b
4 – b
5 – b
6 – a
7 – b
8 – b
9 – b
10 – d


SECTION B – VERY SHORT ANSWERS

11a) 5.7 \times 10^{-5}
11b) 3.94 \times 10^{6}

12 a) 4500
    b) 0.00072


13) 5^{-1} + 2^{-1} = \frac{1}{5} + \frac{1}{2} = \frac{7}{10}


14) m + 5 = 10 \Rightarrow m = 5


15) (8^{1})^{-1} = 8^{-1} = \frac{1}{8}


16) 3^{3} \times 3^{2} = 3^{5}


17)  16


18) 9^{-1} - 3^{-2} = \frac{1}{9} - \frac{1}{9} = 0


19) 0.001 = 10^{-3} \Rightarrow x = -3


20) 6^{-3} = \frac{1}{6^{3}} = \frac{1}{216}


SECTION C – SHORT ANSWERS

21) 11^{8} \times 11^{-5} = 11^{3}


22) 4.2 \times 10^{5} + 0.95 \times 10^{5} = 5.15 \times 10^{5}


23) 2^{-3} \times (2^{2})^{2} \div 2^{-3} = 2^{4} = 16


24) (1/49 - 1/25)^{-1} = -\frac{1225}{24}


25) 5^{4-7+3} = 5^{0} = 1


26)
3^{2} \times 3^{a} = 3^{8} \Rightarrow a = 6


SECTION D – LONG ANSWERS

27) Convert all to base 2:
(Explanation included inside one block)

 \text{Since } 16=2^{4},\ 8=2^{3},\ 4=2^{2},\[4pt] \frac{2^{-8} \times 2^{-3} \times 2^{5}}{2^{-6}} = 2^{-8-3+5+6} = 2^{0} = 1


28a) 1.90 \times 10^{27} + 1.989 \times 10^{30} = 1.9909 \times 10^{30}

28b) \frac{1.989 \times 10^{30}}{1.90 \times 10^{27}} = 1.046 \times 10^{3}

Sun ≈ 1046 times heavier


29)

 x = \frac{(-6)^{-5}}{(-6)^{-2}} = (-6)^{-3}


30a)
3^{,x+1} = 81 = 3^{4} \Rightarrow x = 3

30b)
2^{,x+1} = 64 = 2^{6} \Rightarrow x = 5

Leave A Comment

Your email address will not be published. Required fields are marked *

error: Content is protected !!