Question

Find the value of x.
${( \frac{7}{4} )}^{ - 3} \times { (\frac{7}{4} )}^{ - 5} = { (\frac{7}{4} )}^{x - 2}$
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Answer 1

Answer:

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Answer 2

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$\huge\sf\red{Question\::}$

$\sf Find \:the\: value\: of\: x$

$\sf{( \frac{7}{4} )}^{ - 3}\times { (\frac{7}{4} )}^{ - 5} = { (\frac{7}{4} )}^{x - 2}$

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$\huge\sf\purple{Solution\::}$

$\sf{\bigg( \frac{7}{4} \bigg)}^{ - 3} \times { \bigg(\frac{7}{4} \bigg)}^{ - 5} = { \bigg(\frac{7}{4} \bigg)}^{x - 2}$

$\sf \longrightarrow\:\: { \bigg(\frac{7}{4} \bigg)}^{ - 3 - 5} = { \bigg(\frac{7}{4} \bigg)}^{x - 2} \\\\ \sf \longrightarrow\:\: - 3 - 5 = x - 2 \\\\ \sf \longrightarrow\:\: - 8 = x - 2 \\\\ \sf \longrightarrow\:\: - x = - 2 + 8 \\\\\sf \longrightarrow\:\: - x = 6 \\\\ \sf \longrightarrow\:\: \:x = - 6$

$\sf Hence, \:the\: value\: of\: x\: is\: -6\\\\\:$

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$\Large\sf\green{Additional\: Information\: :}$

$\Large\sf\underline{Few\:important\: Indices}$

• $\large\sf {a}^{m} . \:{a}^{n} = {a}^{m + n}$

• $\large\sf {\Large\frac{ {a}^{m}}{ {a}^{n} }} = {a}^{m - n}$

• $\large\sf( {a}^{m})^{n} = {a}^{mn}$

• $\large\sf {( \frac{a}{b}) }^{m} = \frac{ {a}^{m} }{ {b}^{m} }$

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