25 practice questions on meaning-of-powers from the Power Play section of the UPSC Prelims syllabus.
25 come with a written explanation.
Try the sample set below - the answer stays hidden until you ask for it.
8 Easy12 Medium5 Hard
Sample questions
Q1
easy
What is the value of $17^1$?
A$1$
B$17$
C$34$
D$171$
Show answer and explanation
Correct answer: B - $17$
An exponent of $1$ means the base appears exactly once as a factor, so $17^1 = 17$. The value $1$ mistakes the exponent for the answer, $171$ joins the digits, and $34$ doubles the base.
Q2
easy
How is $9^2$ read aloud?
ANine squared
BNine cubed
CTwo squared
DNine times two
Show answer and explanation
Correct answer: A - Nine squared
A power with exponent $2$ is read as the base 'squared', so $9^2$ is 'nine squared' and equals $81$. 'Two squared' would be $2^2 = 4$, 'nine times two' is $18$, and 'nine cubed' is $9^3$.
Q3
medium
Expand $4^3$ and find its value.
A$64$
B$12$
C$16$
D$43$
Show answer and explanation
Correct answer: A - $64$
Expanding gives $4 \times 4 \times 4 = 64$. Multiplying $4$ by $3$ gives $12$, writing the digits side by side gives $43$, and stopping after two factors gives $16$.
Q4
medium
Consider: (i) $10^3$ means $10$ used as a factor three times. (ii) $10^3$ means $3$ used as a factor ten times. Which is correct?
ANeither (i) nor (ii)
BOnly (i)
CBoth (i) and (ii)
DOnly (ii)
Show answer and explanation
Correct answer: B - Only (i)
The exponent counts how many times the base is used, so $10^3 = 10 \times 10 \times 10 = 1000$ and (i) is true. Statement (ii) describes $3^{10}$, which is $59049$, a completely different value. So only (i) survives.
The $3$ appears twice and the $5$ appears three times, so the product is $3^2 \times 5^3 = 9 \times 125 = 1125$. Swapping the exponents gives $27 \times 25 = 675$. Writing $15^5$ multiplies the bases first, which is wrong, and the last option adds instead of multiplying.
Q6
hard
A student claims that $10^4$ and $4^{10}$ mean the same thing because they use the same two numbers. Which reply corrects her?
AThey are read the same way, but $10^4$ is the larger value
BThey are equal, because both use the digits $10$ and $4$
CThey are read differently, and $10^4 = 10000$ while $4^{10}$ is over a million
DThey are read differently but both come to $40$
Show answer and explanation
Correct answer: C - They are read differently, and $10^4 = 10000$ while $4^{10}$ is over a million
In $10^4$ the base is $10$ used four times, giving $10000$, while in $4^{10}$ the base is $4$ used ten times, giving $1048576$. Swapping base and exponent changes both the reading and the value, so they are neither equal nor both $40$, and $10^4$ is the smaller one here.
Q7
easy
In the power $7^4$, which number is the exponent?
A$4$
B$7$
C$11$
D$28$
Show answer and explanation
Correct answer: A - $4$
The small raised number is the exponent, so here it is $4$, and $7$ is the base. The value $28$ comes from multiplying $7$ by $4$ and $11$ from adding them, but neither is the exponent.
Q8
hard
Which is greater, $3^4$ or $4^3$, and by how much?
A$3^4$ is greater by $17$
B$3^4$ is greater by $7$
CThey are equal
D$4^3$ is greater by $17$
Show answer and explanation
Correct answer: A - $3^4$ is greater by $17$
Expanding gives $3^4 = 81$ and $4^3 = 64$, so $3^4$ wins by $81 - 64 = 17$. The difference is not $7$, and the two are certainly not equal, which shows that swapping base and exponent changes the value.
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