MCQ
laws-of-indices-and-square-cube-roots-l2 MCQ - Practice Questions with Answers
Solve 30 laws-of-indices-and-square-cube-roots-l2 questions for RAS/RPSC preparation.
Practice questions
Q1Which statement gives the meaning of 2^5 for Asha?
2^5 means the base 2 used as a factor five times: 2 x 2 x 2 x 2 x 2 = 32, so option A is correct. Multiplying 2 by 5 (gives 10) or adding 2 five times (gives 10) misreads the exponent; '5 multiplied by itself two times' describes 5^2, not 2^5.
Q2Match the expression with its simplified form. I: (2^3)^2, II: 3^2 x 3^4, III: cube root of 125.
Each item uses a different index law: (2^3)^2 = 2^(3x2) = 2^6 (power of a power multiplies exponents); 3^2 x 3^4 = 3^(2+4) = 3^6 (same base adds exponents); cube root of 125 = 5 because 5^3 = 125. So option A (I-2^6, II-3^6, III-5) is correct; B/C/D mix up these rules.
Q3Imran simplifies 4^3 x 4^2. Which answer is correct?
Same-base multiplication adds the exponents: 4^3 x 4^2 = 4^(3+2) = 4^5, so B is correct. 4^6 wrongly multiplies the exponents (3 x 2); 8^5 and 16^5 wrongly change the base 4 into 8 or 16 instead of keeping it.
Q4Assertion: Expanding 7^5 divided by 7^2 into factors helps explain why the result is 7^3. Reason: Two equal factors of 7 cancel from the numerator and denominator, leaving three factors of 7.
Both parts are true: 7^5 divided by 7^2 becomes five factors of 7 over two factors of 7. Cancelling two common factors leaves three factors of 7, which is 7^3.
Q5Which option correctly defines a perfect square for Class 6 to 8 mathematics?
A perfect square is obtained when a whole number is multiplied by itself, such as 12 times 12. Adding a number to itself gives a double, and three equal factors make a perfect cube; last digits are only a checking clue, not the meaning.
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More questions
6Using the law of indices for multiplication on equal bases, what is the simplified form of 4^3 x 4^2?
7In the index form 6^4, what is the base?
8Assertion: 2^4 x 3^4 can be written as 6^4. Reason: the product law permits a^n b^n = (ab)^n.
9Simplify 3^2 x 3^4 using the same-base multiplication law.
10Match the learner error with the misconception. I: 9^2 = 18, II: square root of 225 = 112.5, III: 5^0 = 0.
11A learner says, 2^4 = 8. Which misconception is most likely shown here?
12Which pair of statements is correct about square and cube roots?
13Devika writes 2^3 x 3^3 as 6^3. Why is this allowed?
14Which statement is incorrect about the laws of indices for non-zero equal bases?
15A learner says, "7^2 = 14." Which teacher question best helps the learner correct the idea?