Question

Solve
If,
25^20x
=
42025 and 64
= 518
Then:
5
(542-1)
(4)-V7
is
B
Previous​

Answer 1

Answer:

Solve

If,

25^20x = 48400 and 64^√ y = 5^18

Then:

(5^(4x-1))5 /(4)-√y is

explanation

\frac{ { {5}^{4x - 1} }^{5} }{ {4}^{ - \sqrt{y} } }

4

−

y

5

4x−1

5

=

{ {5}^{4x - 1} }^{5} = {5}^{20x - 5}5

4x−1

5

=5

20x−5

= { {5}^{2} }^{20x \times \frac{1}{2} } . {5}^{ - 5}=5

2

20x×

2

1

.5

−5

{ 25}^{20x \times \frac{1}{2} } . {5}^{ - 5}25

20x×

2

1

.5

−5

= \sqrt{48400} . {5}^{ - 5}=

48400

.5

−5

= 220. {5}^{ - 5}=220.5

−5

= 44. {5}^{ - 4}=44.5

−4

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

−

y

=4

3

y

3

−1

{64}^{ \sqrt{y} ^{ \frac{ - 1}{3} } }64

y

3

−1

= { {5}^{18} }^{ \frac{ - 1}{3} }=5

18

3

−1

= {5}^{ - 6}=5

−6

total =

\frac{44. {5}^{ - 4} }{ {5}^{ - 6} }

5

−6

44.5

−4

= 44 \times {5}^{2}=44×5

2

=1100

Answer 2

Answer:

If $25^{20x} = 42025$ and $64^{\sqrt{y} } = 5^{18}$ then, $(5^{(4x-1)} )^{5}$/ $4^{-\sqrt{y} }$ is $1025$.

Step-by-step explanation:

we have two equations as follows.

1. $25^{20x} = 42025$
2. $64^{\sqrt{y} } = 5^{18}$

• On simplifying, $(5^{2}) ^{20x} = 42025$

$(5^{20x}) ^{2} = 42025$

$(5^{20x}) = \sqrt{42025} = 205$.

Thus, let  $(5^{20x}) = 205$ be the equation $(1)$.

• On simplifying, $64^{\sqrt{y} } = 5^{18}$

$(4^{3} )^{\sqrt{y} } = 5^{18}$

$(4^{\sqrt{y} })^{3} } = 5^{18}$

$4^{\sqrt{y}} = \sqrt[3]{5^{18}} = 5^{6}$

Thus, $4^{-\sqrt{y}} = \frac{1}{4^{\sqrt{y}}} = \frac{1}{5^{6} }$ and this be the equation $(2)$.

Now, on substituting the R.H.S values from equations (1) and (2),

$(5^{(4x-1)} )^{5}$ / $4^{-\sqrt{y} }$  $= 5^{(20x-5)}$ / $\frac{1}{5^{6} }$

                           $=\frac{ 5^{20x}}{5^{5} . 5^{-6} }$

                           $= \frac{205}{5^{-1} }$

                           $= 205$ x $5$

                           $= 1025$.

Therefore, $(5^{(4x-1)} )^{5}$/ $4^{-\sqrt{y} }$ is $1025$.