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Sagot :
Answer:
n = 6
Step-by-step explanation:
[tex] \frac{ {5}^{n} \times {5}^{3} }{ {5}^{7} } = {5}^{2} \\ \\ \implies \: \frac{ {5}^{n + 3} }{ {5}^{7} } = {5}^{2} \\ \\ \implies \: {5}^{n + 3 - 7} = {5}^{2} \\ \\ \implies \: {5}^{n - 4} = {5}^{2} \\ \\ \implies \:n - 4 = 2 \\ \\ \implies \:n = 4 + 2 \\ \\ \implies \:n = 6[/tex]
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: \frac{5 {}^{n} \times {5}^{3} }{5 {}^{7} } = {5}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \frac{5 {}^{n + 3} {}^{} }{5 {}^{7} } = {5}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:5 {}^{n + 3 - 7} = {5}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:5 {}^{n - 4} = {5}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:{}{n - 4} = {2} [/tex]
[tex]\qquad \sf \dashrightarrow \:n = 2 + 4[/tex]
[tex]\qquad \sf \dashrightarrow \:n = 6[/tex]
Hence, value of n is 6
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