Question

please send me the answer​

Answer 1

Step-by-step explanation:

refer to attachment...

Answer 2

$\sf \dfrac{3^{-4}\times 6^{-3}\times 25 }{10^{-2}\times 16 \times 3^{-6} } \times (6\dfrac{1}{4})^{-2}\times (\dfrac{1}{6})^{-1}$

First of all, we need to represent all numbers in exponential form.

⇒ $\sf \dfrac{3^{-4}\times 6^{-3}\times 5^{2} }{10^{-2}\times 4^{2} \times 3^{-6} } \times (6\dfrac{1}{4})^{-2}\times (\dfrac{1}{6})^{-1}$

⇒ $\sf \dfrac{3^{-4}\times 2^{-3}\times3^{-3}\times 5^{2} }{5^{-2}\times 2^{-2} \times 2^{4} \times 3^{-6} } \times (6\dfrac{1}{4})^{-2}\times (\dfrac{1}{6})^{-1}$

Now we will rearrange the numbers.

⇒ $\sf \dfrac{3^{-4}\times3^{-3}\times 2^{-3}\times 5^{2} }{3^{-6} \times 2^{-2} \times 2^{4} \times 5^{-2} } \times (6\dfrac{1}{4})^{-2}\times (\dfrac{1}{6})^{-1}$

We will apply these laws next ⇒

• $\sf a^m\times a^n=a^{m+n}$

• $\sf a^m\div a^n = \dfrac{a^m}{a^n} = a^{m-n}$

⇒ $\sf \dfrac{3^{(-4+-3)}\times2^{-3}\times 5^{2} }{3^{-6} \times 2^{(-2+4)} \times 5^{-2} } \times (6\dfrac{1}{4})^{-2}\times (\dfrac{1}{6})^{-1}$

⇒ $\sf \dfrac{3^{-7}\times2^{-3}\times 5^{2} }{3^{-6} \times 2^{2} \times 5^{-2} } \times (6\dfrac{1}{4})^{-2}\times (\dfrac{1}{6})^{-1}$

⇒ $\sf (3^{-7-(-6)}\times2^{-3-2}\times 5^{2-(-2)} ) \times (6\dfrac{1}{4})^{-2}\times (\dfrac{1}{6})^{-1}$

⇒ $\sf (3^{-7+6}\times2^{-3-2}\times 5^{2+2} ) \times (6\dfrac{1}{4})^{-2}\times (\dfrac{1}{6})^{-1}$

⇒ $\sf (3^{-1}\times2^{-5}\times 5^{4} ) \times (6\dfrac{1}{4})^{-2}\times (\dfrac{1}{6})^{-1}$

Now we will apply this law next ⇒

• $\sf a^{-m}=\frac{1}{a^m}$

⇒ $\sf (\dfrac{1}{3} \times\dfrac{1}{32} \times 625 ) \times (6\dfrac{1}{4})^{-2}\times (\dfrac{1}{6})^{-1}$

Now we have to convert mixed fraction to improper fraction.

⇒ $\sf (\dfrac{1}{3} \times\dfrac{1}{32} \times 625 ) \times (\dfrac{25}{4})^{-2}\times (\dfrac{1}{6})^{-1}$

Now we will apply this law next ⇒

• $\sf a^{-m}=\frac{1}{a^m}$

⇒ $\sf (\dfrac{1}{3} \times\dfrac{1}{32} \times 625 ) \times (\dfrac{4}{25})^{2}\times (6)$

⇒ $\sf (\dfrac{1}{3} \times\dfrac{1}{32} \times 625 ) \times (\dfrac{16}{625})\times (6)$

⇒ $\sf (\dfrac{1}{96} \times 625 ) \times (\dfrac{16}{625})\times (6)$

⇒ $\sf \dfrac{625}{96} \times \dfrac{16}{625}\times 6$

⇒ $\sf \dfrac{1}{96} \times 16 \times 6$

⇒ $\sf \dfrac{1}{96} \times 96$

⇒ $\sf 1$

∴ $\sf \bf \dfrac{3^{-4}\times 6^{-3}\times 25 }{10^{-2}\times 16 \times 3^{-6} } \times (6\dfrac{1}{4})^{-2}\times (\dfrac{1}{6})^{-1}=1$