laws-of-indices-and-square-cube-roots-l2 MCQ — 10 Practice Questions with Answers

Explanation

The product law a^n b^n = (ab)^n applies only when the exponent is the same on both factors. Here both exponents are 4, so 2^4 x 3^4 = (2 x 3)^4 = 6^4. The assertion and the reason are both true and the reason explains the assertion, so the verdict is D.

Explanation

Same-base division subtracts exponents because equal factors cancel: 7^5 / 7^2 = 7^(5-2) = 7^3. Two of the five 7-factors cancel with the two in the denominator, leaving three. So the assertion and the reason are both true and the reason explains the assertion (option D).

Explanation

2^3 x 3^3 = 6^3 is allowed because the SAME exponent 3 is on both factors (a^n b^n = (ab)^n), not because the bases are equal — they are not. So B is correct. A is wrong (bases differ), C overgeneralises to all unlike bases, and D invents an unrelated addition pattern.

Explanation

Each learner work shows one exact slip: 9^2 = 18 treats the exponent as 9 x 2 (it is 9 x 9 = 81); square root of 225 = 112.5 halves the number (225/2) instead of finding 15^2 = 225; 5^0 = 0 misuses the zero-exponent rule (any non-zero base to power 0 is 1). So option A names all three correctly.

Explanation

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.