Vidaara.orgClass 9 · Mathematics
CodeVID-M9-20-CT
Indices (Exponents) — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
$a^m\cdot a^n=$
- A.$a^{mn}$
- B.$a^{m+n}$
- C.$a^{m-n}$
- D.$a^{m/n}$
2.
$a^{-n}=$
- A.$-a^n$
- B.$\dfrac{1}{a^n}$
- C.$a^n$
- D.$0$
3.
If $a^x=a^y$ ($a\ne0,1$), then:
- A.$x=y$
- B.$x=-y$
- C.$x=1/y$
- D.$xy=1$
4.
$\dfrac{a^m}{a^n}=$
- A.$a^{m+n}$
- B.$a^{m-n}$
- C.$a^{mn}$
- D.$a^{n-m}$
5.
$a^{1/2}=$
- A.$\sqrt a$
- B.$a^2$
- C.$2a$
- D.$\tfrac a2$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Simplify $2^3\times2^2$.
7.
Evaluate $3^{-2}$.
8.
Solve $2^x=16$.
9.
Simplify $\dfrac{5^6}{5^4}$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Simplify $\dfrac{x^5\cdot x^3}{x^2}$.
11.
Evaluate $32^{2/5}$.
12.
Solve $2^x=32$.
13.
Simplify $(2x^2)^3$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Simplify $\dfrac{x^4\cdot x^{-2}}{x^3}$.
15.
Evaluate $\left(\dfrac{16}{81}\right)^{-1/4}$.
Answer Key
Section A — Multiple Choice Questions
- (B) $a^{m+n}$
- (B) $\dfrac{1}{a^n}$
- (A) $x=y$
- (B) $a^{m-n}$
- (A) $\sqrt a$
Section B — Short Answer (2 marks)
- $2^5=32$.
- $\tfrac19$.
- $x=4$.
- $5^2=25$.
Section C — Short Answer (3 marks)
- $x^6$.
- $4$.
- $x=5$.
- $8x^6$.
Section D — Long Answer (5 marks)
- $x^{-1}=\dfrac1x$.
- $\dfrac32$.
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