Surds and Indices

Simplify,

$\frac{{\left(.5\right)}^{{\displaystyle \frac{1}{3}}}\times {\left({\displaystyle \frac{1}{125}}\right)}^{{\displaystyle \frac{1}{4}}}\times {\left(25\right)}^{{\displaystyle \frac{1}{6}}}\times {\left(6.25\right)}^{{\displaystyle \frac{2}{3}}}}{{\left(2.5\right)}^{{\displaystyle \frac{2}{3}}}\times {\left(5\right)}^{-{\displaystyle \frac{1}{2}}}\times {\left({\displaystyle \frac{1}{5}}\right)}^{-2}\times {\left(3125\right)}^{-{\displaystyle \frac{1}{4}}}}$

Simplify,

 $\frac{1}{1+{13}^{7-5}+{13}^{3-5}}+\frac{{\displaystyle 1}}{{\displaystyle 1+{13}^{3-7}+{13}^{5-7}}}+\frac{{\displaystyle 1}}{{\displaystyle 1+{13}^{5-3}+{13}^{7-3}}}$

Arrange the following in descending order,

$2^{196}, 5^{112}, 3^{168}, 4^{140}, 7^{84}$

Simplify,

$\frac{{\left(.0784\right)}^{{\displaystyle \frac{1}{2}}}\times {\left(.1024\right)}^{{\displaystyle \frac{1}{2}}}+1368}{{\left(.001728\right)}^{{\displaystyle \frac{1}{3}}}\times {\left(0.00243\right)}^{{\displaystyle \frac{1}{5}}}}$

Find the value of ${25}^{abc}$ if $x^a=y$, $y^b=z$ and $z^c=x$.

What should come in place of question mark (?) in the following question?

${\left(7\right)}^{8.4}÷{\left(49\right)}^{0.7}={\left(7\right)}^{?+3}÷{\left(343\right)}^3$

What will come in place of the question mark (?) in the given question?

${81}^{2.5} \times 9^{4.5}÷ 3^{4.8} = 9^{?}$

What should come in place of the question mark (?) in the following questions?
$(6{)}^4÷(36{)}^3\times 216=6^{(?-2)}$
 

What will come in place of the question-mark (?) in the following question ?

$$\sqrt { 9216 } \times \sqrt { 2601 } -{ \left( 43 \right) }^{ 2 }=\sqrt { ? } +{ \left( 55 \right) }^{ 2 }$$

What will come in place of the question-mark (?) in the following question ?

$\left[\left(7\sqrt{2}+9\sqrt{2}\right)\times \left(4\sqrt{2}+11\sqrt{2}\right)\right]-257=?$

What will come in place of the question-mark (?) in the following question ?

$$\frac { 14 }{ 39 } \times \frac { 117 }{ 154 } \div \frac { 78 }{ 88 } +\frac { 15 }{ 78 } =?$$

What will come in place of the question-mark $(?)$ in the following question ?

${\left(17.3\right)}^2+{\left(37.2\right)}^2-{\left(32.6\right)}^2=?+437.21$

What will come in place of the question-mark (?) in the following question ?

If a-b= 3 and a² + b² = 29, then ab=?