Laws of exponents Quiz - ICSE Class 7 Mathematics

Free practice quiz: Laws of exponents (ICSE Class 7 Mathematics). 51 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

Sample questions

1. Simplify: $(7^5 \times 7^3) / 7^4$

   1. $7^2$
   2. $7^4$
   3. $7^8$
   4. $7^{15}$
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   Answer: B. $7^4$

   Using the law of exponents $a^m \times a^n = a^{m+n}$ and $a^m / a^n = a^{m-n}$, we have $(7^5 \times 7^3) / 7^4 = 7^{5+3} / 7^4 = 7^8 / 7^4 = 7^{8-4} = 7^4$.

2. Simplify: $a^3 \times a^5 \times a^2$

   1. $a^{10}$
   2. $a^{30}$
   3. $a^6$
   4. $a^{-2}$
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   Answer: A. $a^{10}$

   Using the law of exponents $a^m \times a^n = a^{m+n}$, we have $a^3 \times a^5 \times a^2 = a^{3+5+2} = a^{10}$.

3. Evaluate: $(6^2)^3 / 6^4$

   1. $6^2$
   2. $6^3$
   3. $6^8$
   4. $6^{-2}$
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   Answer: A. $6^2$

   Using the laws of exponents, $(6^2)^3 / 6^4 = 6^{2 imes 3} / 6^4 = 6^6 / 6^4 = 6^{6-4} = 6^2$.

4. Simplify: $9^5 / 9^5$

   1. $9^0$
   2. 1
   3. $9^{25}$
   4. 0
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   Answer: A. $9^0$

   Using the law of exponents $a^m / a^n = a^{m-n}$, we have $9^5 / 9^5 = 9^{5-5} = 9^0$. Since any non-zero number raised to the power of 0 is 1, $9^0 = 1$.

5. Simplify: $(4^{-2})^3 / 4^{-5}$

   1. $4^{-11}$
   2. $4^{-1}$
   3. $4^1$
   4. $4^{-2}$
   Show answer

   Answer: B. $4^{-1}$

   Using the laws of exponents, $(4^{-2})^3 / 4^{-5} = 4^{-2 imes 3} / 4^{-5} = 4^{-6} / 4^{-5} = 4^{-6 - (-5)} = 4^{-6+5} = 4^{-1}$.

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