Delhi Police Constable Exam Model Paper 10

By using the law of indices∶
Laws of Indices∶-
1-∶ ${\mathit{a}}^{\mathit{m}}\times {\mathit{a}}^{\mathit{n}}={\mathit{a}}^{\mathit{m}+\mathit{n}}$
$2-:{\mathit{a}}^{\mathit{m}}÷{\mathit{a}}^{\mathit{n}}={\mathit{a}}^{\mathit{m}\mathit{–}\mathit{n}}$
$3-:$[(a^m)^n] = a^{mn}$
4-∶ (a)^{(1/m)}=m_√a$
$5-:{\left(\mathit{a}\right)}^{\left(-\mathit{m}\right)}=\frac{1}{{\mathit{a}}^{\mathit{m}}}$
$6-:{\left(\mathit{a}\right)}^{\left(\frac{\mathit{m}}{\mathit{n}}\right)}={\mathit{n}}_{\sqrt{{\mathit{a}}^{\mathit{m}}}}$
7-∶ ${\left(\mathit{a}\right)}^0=1$
The equation will be solved as
${25}^{4.1}÷5^{3.3}\times {125}^{6.7}={25}^{\mathit{X}}$
⇒ ${\left(5^2\right)}^{4.1}÷5^{3.3}\times {\left(5^3\right)}^{6.7}={\left(5^2\right)}^{\mathit{X}}$
⇒ $5^{8.2}÷5^{3.3}\times 5^{20.1}=5^{2\mathit{X}}$
⇒ $5^{\left(8.2\mathit{–}3.3\right)}\times 5^{20.1}=5^{2\mathit{X}}$
⇒ $5^{4.9}\times 5^{20.1}=5^{2\mathit{X}}$
⇒ $5^{\left(4.9+20.1\right)}=5^{2\mathit{X}}$
⇒ $5^{25}=5^{2\mathit{X}}$
⇒ $25=2\mathit{X}$
$\therefore \mathit{X}=12.5$