Question

Answer step by step

Answer 1

Step-by-step explanation:

$concept = \\ {a}^{m} \div {a}^{n} = {a}^{m - n} only \: when \: m \: is \: bigger \: than \: n$

$concept = \\ {a}^{m} \times {a}^{n} = {a}^{m + n}$

so using these

q3》

$\frac{ {7}^{1} }{ {8}^{16} } \div \frac{ {7}^{1} }{ {8}^{14} } \\ = \frac{ {7}^{1 - 1} }{ {8}^{16 - 14} } \\ = \frac{ {7}^{0} }{ {8}^{2} } = \frac{1}{64}$

q4》

$( {2}^{4} \times {2}^{5} ) \div ( {2}^{2} \times {2}^{3} ) \\ = {2}^{5 + 4} \div {2}^{2 + 3} \\ {2}^{9} \div {2}^{5} \\ = {2}^{9 - 5} \\ = {2}^{4} = 16$

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Answer 2

Answer:

25^x-1 = 5^2x-1 - 100

⇒ 5^2x-2 = 5^(2x-1) - 100

⇒ 5^2x-2 - 5^2x-1 = -100

⇒ 5^2x [ 5^-2 - 5^-1] = - 100

⇒ 5^2x [ 1 - 1 ] = - 100

25 5

⇒ 5^2x [ 1 - 5 ] = - 100

25

⇒ 5^2x [ -4 ] = - 100

25

⇒ 5^2x [-4] = -100 * 25

⇒ 5^2x = 100 * 25 [ - * - = +]

4

⇒ 5^2x = 625

⇒ 5^2x = 5^4

so, ⇒ 2x = 4

⇒ x=2

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