Question

Consider the following statements.

(i) $\frac{2^7}{5^7}={\left(\frac{2}{5}\right)}^7$

(ii) $2^7\times 5^7=(25{)}^7$

• A. (i) is true and (ii) is false.
• B. (i) is false and (ii) is true.
• C. Both statements are false.
• D. Both statements are true.

Answer 1

The correct option is A (i) is true and (ii) is false.

Using the law of exponents $\frac{a^m}{b^m}=(\frac{a}{b}{)}^m,$ we have
$⟹\frac{2^7}{5^7}={\left(\frac{2}{5}\right)}^7.$

Using the law of exponents $a^m\times b^m=(ab{)}^m,$
$2^7\times 5^7=(2\times 5{)}^7={10}^7\ne {25}^7.$

Hence, statement (i) is true and statement (ii) is false.