Question

answer is given question​

Answer 1

Answer :-

• First u need to know some identities :-

$\longrightarrow\large\textsf{ a^{m} × a^{n} = a^{m + n } }$

$\longrightarrow\large\textsf{ a^{m} ÷ a^{n} = a^{m - n } }$

Now we apply this identities for this sum :-

$= \: \: \: \: \: \: \: \frac{ { 3}^{ - 5} \times {10}^{ - 5} \times 125 }{ {5}^{ - 7} \times {6}^{ - 5} } \\ \\ = \: \: \: \: \: \: \: \: \: \frac{ \cancel{{3}^{ - 5}} \times \cancel{{2}^{ - 5}} \times {5}^{ - 5} \times {5}^{3} }{ {5}^{ - 7} \times \cancel{{3}^{ - 5}} \times \cancel{{2}^{ - 5}} } \\ \\ = \: \: \: \: \: \: \: \: \: \frac{ {5}^{ - 5 + 3} }{ {5}^{ - 7} } \\ \\ = \: \: \: \: \: \: \: \frac{ {5}^{ - 2} }{ {5}^{ - 7} } \\ \\ = \: \: \: \: \: {5}^{ - 2 - ( - 7)} \\ \\ = \: \: \: \: \: \: {5}^{ - 2 + 7} \\ \\ = \: \: \: \: \: \boxed{{5}^{5}}$

Answer 2

Answer:

First u need to know some identities :-

\longrightarrow\large\textsf{$ a^{m} × a^{n} = a^{m + n }$}⟶a

m

×a

n

=a

m+n

\longrightarrow\large\textsf{$a^{m} ÷ a^{n} = a^{m - n }$}⟶a

m

÷a

n

=a

m−n

Now we apply this identities for this sum :-

\begin{gathered} = \: \: \: \: \: \: \: \frac{ { 3}^{ - 5} \times {10}^{ - 5} \times 125 }{ {5}^{ - 7} \times {6}^{ - 5} } \\ \\ = \: \: \: \: \: \: \: \: \: \frac{ \cancel{{3}^{ - 5}} \times \cancel{{2}^{ - 5}} \times {5}^{ - 5} \times {5}^{3} }{ {5}^{ - 7} \times \cancel{{3}^{ - 5}} \times \cancel{{2}^{ - 5}} } \\ \\ = \: \: \: \: \: \: \: \: \: \frac{ {5}^{ - 5 + 3} }{ {5}^{ - 7} } \\ \\ = \: \: \: \: \: \: \: \frac{ {5}^{ - 2} }{ {5}^{ - 7} } \\ \\ = \: \: \: \: \: {5}^{ - 2 - ( - 7)} \\ \\ = \: \: \: \: \: \: {5}^{ - 2 + 7} \\ \\ = \: \: \: \: \: \boxed{{5}^{5}} \end{gathered}

=

5

−7

×6

−5

3

−5

×10

−5

×125

=

5

−7

×

3

−5

×

2

−5

3

−5

×

2

−5

×5

−5

×5

3

=

5

−7

5

−5+3

=

5

−7

5

−2

=5

−2−(−7)

=5

−2+7

=

5

5