Question

Evaluate: $(7^{-\frac{1}{2}}\times 5^2{)}^2÷\sqrt{{25}^3}=$

• A. $\frac{5}{7}$
• B. $\frac{7}{5}$
• C. 35
• D. $-\frac{5}{7}$

Answer 1

The correct option is A $\frac{5}{7}$

$(7^{-\frac{1}{2}}\times 5^2{)}^2÷\sqrt{{25}^3}$

$\Rightarrow$ $(7^{-1}\times 5^4)÷\sqrt{15625}$

$\Rightarrow$ $\frac{1}{7}\times 625÷125$

$\Rightarrow$ $\frac{625}{7}\times \frac{1}{125}$

$\Rightarrow$ $\frac{5}{7}$

$\therefore$ $(7^{-\frac{1}{2}}\times 5^2{)}^2÷\sqrt{{25}^3}=\frac{5}{7}$