#### Solved Examples and Worksheet for Using Laws of Exponents

Q1Which one shows 11 × 11 × 11 × 11 × 11 × 11 written in exponential form?

A. 116
B. 135
C. 126
D. 115

Step: 1
11 × 11 × 11 × 11 × 11 × 11 = 116
[11 is used 6 times as a factor.]
Q2If we express 6 × 6 × 6 using an exponent, what would be the base?

A. 6
B. 4
C. 3
D. None of the above

Step: 1
6 × 6 × 6 = 63
[6 is repeated 3 times as a factor.]
Step: 2
The base is 6.
Q3Identify the expression 5 -2 as a fraction.

A. 1- 52
B. 152
C. - 52
D. 153

Step: 1
5 -2 = 152
[A base with negative exponent is expressed as a-n = 1an.]
Step: 2
The expression 5 - 2 in the form of fraction is 152.
Q4Express the expression (- 3)-4 in fraction form.
A. - 181
B. 181
C. - 127
D. 127

Step: 1
(- 3)-4
[Original expression.]
Step: 2
= 1(- 3)4
[A base with negative exponent is expressed as a- n = 1an.]
Step: 3
= 1(- 3)4 = 181
Step: 4
The expression (-3)-4 is equal to 181 in fraction form.
Q5Identify the expression - (5)- 3 as a fraction.
A. - 1125
B. 125
C. 1125
D. None of the above

Step: 1
- (5)- 3 = - 153
[A base with negative exponent is expressed as a- n = 1an.]
Step: 2
(5)3 = 125
Step: 3
- 153 = - 1125
Step: 4
The expression - (5)- 3 in the form of fraction is - 1125.
Correct Answer is :   - 1125
Q6Identify 42 × 47 using single exponent.
A. - 49
B. 49
C. 414
D. 47

Step: 1
42 × 47 = 4(2 + 7) = 49
Step: 2
The expression 42 × 47 in single exponent form is 49.
Q7Identify 44 × 45 using single exponent.

A. - 45
B. - 44
C. 49
D. 420

Step: 1
44 × 45 = 4(4 + 5)
Step: 2
= 49
[Simplify.]
Step: 3
The expression 44 × 45 in single exponent form is 49.
Q8Identify 7172 × 7172 × 7172 in exponential form.
A. 7172
B. 71722
C. 3 × 7172
D. 71723

Step: 1
7172 × 7172 × 7172 = 71723
[7172 is used 3 times as a factor.]
Q9Identify the equivalent of (- d)- 6 expressed using a positive exponent.
A. 1d6
B. - 1d6
C. d6
D. None of these

Step: 1
(- d)-6
[Original expression.]
Step: 2
= 1(- d)6
[By definition of a negative exponent a- n = 1an]
Step: 3
= 1d6

Step: 4
The expression (- d)-6 using a positive exponent is 1d6 .
Q10Find the value of a in the equation 73 × 7a = 77 .
A. 4
B. 5
C. 3
D. 6

Step: 1
73 × 7a = 77
[Original equation.]
Step: 2
= 73 + a = 77
[Use product of powers property.]
Step: 3
3 + a = 7
[Since the bases are same, the powers should be equal.]
Step: 4
a = 7 - 3 = 4
[Simplify.]
Step: 5
The value of a is 4 .
Q11Which of the following expression is equivalent to 53 × 54?
A. 512
B. 57
C. 257
D. 2512

Step: 1
53 × 54 = 5(3 + 4)
[Use product of powers property.]
Step: 2
= 57
Step: 3
53 × 54, expressed as single power of the base is 57.
Q12Simplify:
(-5)3(-5)7

A. 625
B. (-5)3
C. 1-625
D. 1625

Step: 1
(-5)3(-5)7
[Original expression.]
Step: 2
= (-5)3 - 7
[Use quotient of powers property.]
Step: 3
= (-5)-4
[Subtract exponents.]
Step: 4
= 1(-5)4
[Use definition of negative exponent.]
Step: 5
= 1625
[Evaluate power.]
Q13Evaluate the expression 4 - 2.

A. 14
B. 116
C. 4
D. 16

Step: 1
4- 2
[Original expression.]
Step: 2
= 1(4)2
[Use the rules for negative exponents.]
Step: 3
= 116
[Evaluate the power.]
Step: 4
The value of the expression is 116.
Q14Evaluate the expression.
7 - 5 × 710

A. 117649
B. 16807
C. 1117649
D. 116807

Step: 1
7 - 5 × 710 = 7 - 5 + 10
[Use the product of powers property.]
Step: 2
= 75
Step: 3
= 16807
[Evaluate the power.]
Step: 4
The value of the expression is 16807.
Q15Evaluate the expression.
(- 3)- 4 × (- 3)2

A. 19
B. 13
C. 9
D. 3

Step: 1
(- 3)- 4 × (- 3)2 = (- 3)- 4 + 2
[Use the product of powers property.]
Step: 2
= (- 3)- 2