1. Simplify: 2³ x 2⁴
- A2⁷
- B2¹2
- C4⁷
- D2¹
Show answer
Answer: A) 2⁷
When bases are equal, add the powers: 2³ x 2⁴ = 2^(3+4) = 2⁷.
Class 7 Laws of Exponents — practice questions with answers
Number System · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. Simplify: (2³ x 2²)²
- A2¹0
- B2⁷
- C2¹2
- D2²5
Show answer
Answer: A) 2¹0
Inside: 2³ x 2² = 2⁵. Then (2⁵)² = 2^(5x2) = 2¹0.
3. A scientist describes a bacteria culture.
At the start there are 2⁴ bacteria.
The count later becomes 2⁴ multiplied by itself 3 times (i.e. (2⁴)³).
Express the final count as a single power of 2.
At the start there are 2⁴ bacteria.
The count later becomes 2⁴ multiplied by itself 3 times (i.e. (2⁴)³).
Express the final count as a single power of 2.
- A2¹2
- B2⁷
- C2⁶4
- D2⁹
Show answer
Answer: A) 2¹2
(2⁴)³ = 2^(4x3) = 2¹2 by the power-of-a-power rule.
4. On Diwali, Anita lights diyas in a pattern.
The first row has 4² diyas, and each next row has 4 times the diyas of the previous row.
How many diyas are in the third row? Give the answer as a single power of 4.
The first row has 4² diyas, and each next row has 4 times the diyas of the previous row.
How many diyas are in the third row? Give the answer as a single power of 4.
- A4⁴
- B4⁶
- C4⁵
- D4⁸
Show answer
Answer: A) 4⁴
Row 1: 4². Row 2: 4² x 4 = 4³. Row 3: 4³ x 4 = 4⁴.
5. Anjali has to find the unknown power n in the equation:
(3^n x 3⁴) / 3² = 3⁹
Work through the laws of exponents to find n.
(3^n x 3⁴) / 3² = 3⁹
Work through the laws of exponents to find n.
- A7
- B6
- C14
- D8
Show answer
Answer: A) 7
Left side: (3^n x 3⁴) / 3² = 3^(n+4) / 3² = 3^(n+4-2) = 3^(n+2). Setting n+2 = 9 gives n = 7.
Practise all 50 questions free →
10 free questions a day without an account — unlimited with a free account.