Simplification for IBPS PO test 6-Solved questions with detailed explanations for SSC, IBPS PO, SBI PO, RRB, RBI, CSE, CGL, CHSL, CDA, CSE, UPSC

11)

What will come in place of question mark (?) in the following questions

${(98)}^{45} \times {(98)}^{-35} =?$

[OBC (PO), 2008]

A)
98
B)
${(98)}^{2}$
C)
${(98)}^{- 5}$
D)
${(98)}^{10}$
E)
None of these

Answer: Option D

Explanation

$\begin{array}{l} Here \\ {= (98)}^{45} \times {(98)}^{-35} \\ By the rule of indices, we get \\ {= 98}^{45-35} {= (98)}^{10} \end{array}$

Hence, Option D is correct.

Discussion

12)

${(31)}^{3} \times {(31)}^{-27} =?$

[AndhraBank (PO), 2008]

A)
${(961)}^{2}$
B)
4
C)
${(31)}^{2}$
D)
29791
E)
None of these

Answer: Option A

Explanation

$\begin{array}{l} Here, \\ {= (31)}^{3} \times {(31)}^{-27} \\ By the rule of indices, we get \\ {= (33)}^{31- 27} {= (31)}^{4} \\ {= (961)}^{2} [∵ 31^{2} = 961] \end{array}$

Hence, Option A is correct.

Discussion

13)

${(32)}^{20} \div {(32)}^{5} =?$

[AndhraBank (PO), 2008]

A)
${(32)}^{100}$
B)
${(32)}^{2}$
C)
${(32)}^{25}$
D)
${(32)}^{15}$
E)
None of these

Answer: Option D

Explanation

$\begin{array}{l} Here, \\ By applying the rule of indices \\ we get, \\ {= ? = (32)}^{20} \div {(32)}^{5} \\ {= ? = (32)}^{20}^{- 5} {= (32)}^{15} \end{array}$

Hence, Option D is correct.

Discussion

14)

${(27)}^{18} \div {(27)}^{3}$

[AndhraBank (PO), 2008]

A)
${(27)}^{54}$
B)
${(27)}^{21}$
C)
${(27)}^{15}$
D)
${(27)}^{6}$
E)
None of these

Answer: Option C

Explanation

$\begin{array}{l} Here, \\ \Rightarrow {(27)}^{18} {+ (27)}^{3} [∵ a^{m} \div a^{n} = a^{m - n}] \\ \Rightarrow {(27)}^{18-3} {=(27)}^{15} \end{array}$

Hence, Option C is correct.

Discussion

15)

${(19)}^{29} \times {(19)}^{-27} =?$

[Union Bank of India (PO), 2008]

A)
6
B)
361
C)
19
D)
6859
E)
None of these

Answer: Option B

Explanation

$\begin{array}{l} Here, \\ {= (19)}^{29} \times {(19)}^{- 27} \\ [∵ a^{m} \times a^{n} = a^{m + n}] \\ = {(19)}^{29 - 27} = {(19)}^{2} = 361 \end{array}$

Hence, Option B is correct.

Discussion

Simplification-Test 6 (Based on Surds and Indices/Percentages)

Answer: Option D

Answer: Option A

Answer: Option D

Answer: Option C

Answer: Option B