Question

what is the value of (5^-2×10^-4)/(2^-5×5^-6)​

Answer 1

Answer:

5^-2 =1/5^2

(1/25*1/10000)/(1/32*1/15625)

=32*15625/25*10000

for simplicity write

32=8*4

15625=25*25*25

10000=100*100

8*4*25*25*25/25*100*100= 2

Step-by-step explanation:

Answer 2

Correct Question:

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

Answer:

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

$= \: \sf \: \dfrac {{(2)}^{ 5} \: \times \: {(5)}^{ 6} }{ {(10)}^{ 4} \: \times \: {(5)}^{ 2} }$

$\: \sf [ by \: using \: {a}^{ - 1} \: = \: \dfrac{1}{a} ]$

$= \: \sf \: \dfrac {{(2)}^{ 5} \: \times \: {(5)}^{ 6} }{ {(5 \times 2)}^{ 4} \: \times \: {(5)}^{ 2} }$

$\: \sf [ by \: using \: {(a \times b)}^{ m} \: = \: ( {a}^{m} \: \times \: {b}^{m} ) ]$

$= \: \sf \: \dfrac {{(2)}^{ 5} \: \times \: {(5)}^{ 6} }{ {5}^{4} \times {2}^{ 4} \: \times \: {(5)}^{ 2} }$

$= \: \sf \: {(2)}^{ 5 \: - \: 4} \: \times \: {(5)}^{ 6 \: - \: 6}$

$\: \sf [ by \: using \: \dfrac{ {a}^{m} }{ {a}^{n} } \: = \: {a}^{m - n} ]$

$= \: \sf \: (2) \: \times \: {(5)}^{ 0}$

$= \: \sf \: (2) \: \times \: 1$

$\: \sf [ by \: using \: {a}^{0} \: = \: 1]$

$\sf = \: \boxed{2}$

$\sf\blue{Hope\:This\:Helps\:!\:}$