Question 1.
Fill in the blanks:-
i. Any non-zero number with exponent zero is equal to _____________
ii. $2^x = 16$, then x is _______
iii. Writing repeated multiplication of numbers in a short form is called ___________________
iv. a raised to the power 2 is called a _______________ and a raised to the power 3 is called a ___________
v. if base is negative and exponent is odd, the expression has ______________ value.
Question 2.
State true or false:-
i. $(a \div a) \times a = a$; for every non-zero rational number
ii. $a^5 \times b^5 = ab^5$
iii. $b^{12} \times (-b)^6 = b^{18}$
iv. 2 is the base of exponential expression $(-2)^{10}$ .
v. $2^4 \times 2^3 = 6^7$
vi . $1^0 \times 0^1 = 1$
vii. $3^4 > 4^3$
viii. $4^0 + 5^0 + 6^0 = (4 + 5 + 6)^0$ Question 3
if $4^x = 64$, then find the value of $12^{2x-6}$
Question 4.
Find x if
i. $11^6 \div 11^{4-x} = 11^8$
ii. $(-3)^{x-2} = -243$
Question 5.
Simplify and express as a power of a rational number.
i. $(\frac {4}{3})^2 \times (\frac {2}{3})^3 \times \frac {1}{4}$
ii. $\left [ \left ( \frac{-3}{5} \right )^2 \times \left ( \frac{-3}{5} \right )^4 \right ]^3$
iii. $ \frac {3^5 \times 10^5 \times 25}{5^7 \times 6^5}$
iv. $\frac {3^8 \times a^6}{9^3 \times a^3}$
Question 6.
Evaluate:-
i. $(9^0 \times 7^0) \times (9 +7)$
ii. $ \frac {(-8)^0 - 11^0}{ (\frac {-2}{3})^0}$
iii.$(-1)^{10} \times (-1)^5 \times (-1)^4$
iv. $(-1)^{12} - (-1)^7$
Question 7.
Write in standard form;
i) 7489.3 ii) 6,780,000
iii) 8,04,000 iv) 78,950 Question 8
a is a non-zero rational number. Product of the square of a with the cube of a is equal to the
(a) second power of a
(b) third power of a
(c) fifth power of a
(d) sixth power of a Question 9
Which of the follwing is equal to 1?
(a) $2^0 + 3^0 + 4^0$
(b) $2^0 \times 3^0 \times 4^0$
(c) $(3^0 – 2^0) \times 4^0$
(d) $(3^0 – 2^0) \times (3^0 +2^0)$ Question 10
Which of the two is larger : $3^{12}$ or $6^6$ ?
Answer
1.
a. 1
b. 4
c. power notation
d. square,cube
e. negative
2.
i.True
ii. False
iii. True
iv. False
v. False
vi. False
vii. True
viii. false
3. 1
4.
i. x=6
ii. x=7
5.
i. $(\frac {2}{3})^5$
ii. $(\frac {3}{5})^{18}$
iii. 1
iv. $ \frac {a^3}{3}$
6.
i. 16
ii. 0
iii. -1
iv. 2
8. c
9. b
10. $3^{12}$
