Q 1 Mathematics Surds And Indices
Simplify (27)^(2/3):
View answer & explanation Ans: 9
Correct Answer: 9
(27)^(2/3) = (3^3)^(2/3) = 3^2 = 9.
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Arithmetic: Surds and Indices — Solved MCQs Solved MCQs
Solved surds and indices MCQs — 16 questions on fractional exponents, negative exponents, surd simplification and index laws, with verified answers and explanations. Free online practice for FPSC, PPSC, NTS and all one-paper exams. Covers surds and indices.
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About this paper
This is the Arithmetic: Surds and Indices solved MCQ bank from Advanced FPSC & Other Federal Model Papers (Edition 32): 16 published questions (book pp. 779-780, all 16 printed) on fractional and negative exponents, surd simplification, powers of powers and index laws. Every answer was re-solved from scratch against the printed Answer Key, and every question carries a worked explanation.
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Arithmetic: Surds and Indices — Solved MCQs
Read mode 16 MCQs · 16 minutes
Subject 1
Mathematics
1
Topic Section
Surds And Indices
16 solved MCQs shown directly below
Q 2 Mathematics Surds And Indices
Evaluate (256)^0.16 x (16)^0.18
View answer & explanation Ans: 4
Correct Answer: 4
256 = 2^8 and 16 = 2^4, so the product is 2^1.28 x 2^0.72 = 2^2 = 4.
Q 3 Mathematics Surds And Indices
The value of (256)^(5/4) is:
View answer & explanation Ans: 1024
Correct Answer: 1024
(256)^(5/4) = (4^4)^(5/4) = 4^5 = 1024.
Q 4 Mathematics Surds And Indices
The value of (sqrt(8))^(1/3) is:
View answer & explanation Ans: sqrt(2)
Correct Answer: sqrt(2)
(sqrt(8))^(1/3) = 8^(1/6) = (2^3)^(1/6) = 2^(1/2) = sqrt(2).
Q 5 Mathematics Surds And Indices
The value of (32/243)^(-4/5) is:
View answer & explanation Ans: 81/16
Correct Answer: 81/16
32/243 = (2/3)^5, so (32/243)^(-4/5) = (2/3)^(-4) = (3/2)^4 = 81/16.
Q 6 Mathematics Surds And Indices
The value of (-1/216)^(-2/3) is:
View answer & explanation Ans: 36
Correct Answer: 36
The cube root of -1/216 is -1/6; squared it gives 1/36, and the negative exponent inverts it to 36.
Q 7 Mathematics Surds And Indices
The value of 5^(1/4) x (125)^0.25 is:
View answer & explanation Ans: 5
Correct Answer: 5
125 = 5^3, so the product is 5^(1/4) x 5^(3/4) = 5^1 = 5.
Q 8 Mathematics Surds And Indices
(1/216)^(-2/3) x (1/27)^(4/3) = ?
View answer & explanation Ans: 4/9
Correct Answer: 4/9
(1/216)^(-2/3) = 36 and (1/27)^(4/3) = 1/81, so the product is 36/81 = 4/9.
Q 9 Mathematics Surds And Indices
(1000)^7 / 10^18 = ?
View answer & explanation Ans: 1000
Correct Answer: 1000
(1000)^7 = (10^3)^7 = 10^21, and 10^21 / 10^18 = 10^3 = 1000.
Q 10 Mathematics Surds And Indices
(256)^0.16 x (256)^0.09 = ?
View answer & explanation Ans: 4
Correct Answer: 4
Same base, so add the exponents: 256^(0.16 + 0.09) = 256^0.25 = 4.
Q 11 Mathematics Surds And Indices
(0.04)^(-1.5) = ?
View answer & explanation Ans: 125
Correct Answer: 125
0.04 = 1/25, so (1/25)^(-3/2) = 25^(3/2) = 125.
Q 12 Mathematics Surds And Indices
49 x 49 x 49 x 49 = 7^?
View answer & explanation Ans: 8
Correct Answer: 8
49 = 7^2, so 49^4 = 7^8.
Q 13 Mathematics Surds And Indices
The value of (8^(-25) - 8^(-26)) is:
View answer & explanation Ans: 7 x 8^(-26)
Correct Answer: 7 x 8^(-26)
Factor out 8^(-26): 8^(-25) - 8^(-26) = 8^(-26) x (8 - 1) = 7 x 8^(-26).
Q 14 Mathematics Surds And Indices
(64)^(-1/2) - (-32)^(-4/5) = ?
View answer & explanation Ans: 1/16
Correct Answer: 1/16
(64)^(-1/2) = 1/8 and (-32)^(-4/5) = 1/16 (since the fifth root of -32 is -2), so the difference is 1/8 - 1/16 = 1/16.
Q 15 Mathematics Surds And Indices
If sqrt(2^n) = 64, then the value of n is:
View answer & explanation Ans: 12
Correct Answer: 12
sqrt(2^n) = 2^(n/2) = 64 = 2^6, so n/2 = 6 and n = 12.
Q 16 Mathematics Surds And Indices
If m and n are whole numbers such that m^n = 121, then the value of (m - 1)^(n + 1) is:
View answer & explanation Ans: 1000
Correct Answer: 1000
121 = 11^2, so m = 11 and n = 2, giving (11 - 1)^(2 + 1) = 10^3 = 1000.
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Paper practice FAQs
How many questions are in the Arithmetic: Surds and Indices MCQ bank? +
16 questions, all 16 printed in the book. No item was dropped: every keyed answer was verified by re-solving.
What does the Surds and Indices bank cover? +
Fractional exponents such as (27)^(2/3), negative exponents, surd simplification such as (sqrt(8))^(1/3), products of powers with the same base, and solving for an unknown exponent in equations like sqrt(2^n) = 64.
Are the answers verified? +
Yes. Every published answer was re-solved from scratch and checked against the book's printed Answer Key on p. 780; all 16 published answers agree with the key. Four items carry reading notes rather than overrides: the exponent signs in two questions and one option's exponent were confirmed by zooming the scan to 300 DPI before accepting the keyed answer.
Which other exams does this bank help with? +
Surds and indices questions of this form appear in FPSC, PPSC, NTS, OTS and other one-paper exams, as well as CSS MPT-style quantitative sections, so the bank is tagged for all of them.