Question

if 25^20x=40804 and 64√y=5^18 then(54x-1)5

Answer 1

Answer:

260 is correct answer

Step-by-step explanation:

(54x-1)5

(270x-5)

=260

is solution

Answer 2

If $25^{20x}=40804$ and $64\sqrt{y} =5^{18}$ then$\frac{ (54x-1)5}{4^{-\sqrt{y} } }$is 1100

Step-by-step explanation:

Given: $25^{20x}=40804$ and $64\sqrt{y} =5^{18}$

To find: The value for $\frac{ (5^{4x-1})^{5} }{4^{-\sqrt{y} } }$

Formula used:

1) $a^{m} .a^{n} =a^{m+n}$

2) $\frac{a^{m} }{a^{n} } =a^{m-2}$

3) $(a^{m} )^{n} =a^{mn}$

Solution:

Given, $\frac{ (5^{4x-1})^{5} }{4^{-\sqrt{y} } }$

According to the given equation, we can use the third formula mentioned above.

$(5^{4x-1})^{5}$= $5^{20x-5}$

$= > 5^{20x}(5^{-5})$

Multiply and divide with 2

$= > 5^{2*20*\frac{1}{2} } (5^{-5})$

$= > 25^{20x*\frac{1}{2} } (5^{-5})$

Given equation $25^{20x}=40804$

Apply it,

$= > \sqrt{40804} .5^{-5}$   (Power $\frac{1}{2}$ become square root here)

The value for $\sqrt{40804}$ is 220.

$= > 220(5^{-5})$

Now 220 can be written as $44*5$

$= > 44*5( 5^{-5})$

$= > 44(5^{-4})$

Now, to find $4^{-\sqrt{y}$

$= > 4^{3\sqrt{y}*\frac{-1}{3} }$

$= > 64\sqrt{y} *\frac{-1}{3}$

$= > 5^{18} *\frac{-1}{3}$

$= > 5^{-6}$

Now apply the values that were found out above in the given equation

$\frac{ (54x-1)5}{4^{-\sqrt{y} } }=\frac{ 44(5^{-4})}{5^{-6}}$

$= > 44(5^{-4+6} )$

$= > 44(5^{2})$

$= > 44*25$

$= > 1100$

Hence, If $25^{20x}=40804$ and $64\sqrt{y} =5^{18}$ then $\frac{ (54x-1)5}{4^{-\sqrt{y} } }$ is 1100