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Exponents — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSExponents1 Mark
MCQ
Assertion (A): $\left(\frac{2}{3}\right)^2 \times\left(\frac{2}{3}\right)^3=\left(\frac{2}{3}\right)^5$
Reason (R): For any rational number $\frac{a}{b}$, we have $\left\{\left(\frac{a}{b}\right)^m\right\}^n=\left(\frac{a}{b}\right)^{m n}$.
  • A
    Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanatton of Assertion (A).
  • ✓
     Both Assertion (A) and Reason (R) are true and Reason (R) Is not the correct explanatlon
    of Assertion (A). 
  • C
    Assertion (A) is true but Reason (R) is false.
  • D
    Assertion (A) is false but Reason (R) is true.
✓

Answer

Correct option: B.
 Both Assertion (A) and Reason (R) are true and Reason (R) Is not the correct explanatlon
of Assertion (A). 
(b): A is true since $\left(\frac{a}{b}\right)^m \times\left(\frac{a}{b}\right)^n=\left(\frac{a}{b}\right)^{m+n}$ for any rational number $\left(\frac{a}{b}\right)$ and positive integers $m$ and $n . R$ is clearly true by the laws of exponents.
$\therefore A$ and R are both true but R is not the correct explanation of A .

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