Question

*व्यंजक 2¹³/8³ पर विचार कीजिए। दिए गए व्यंजक का मान ज्ञात करने का पहला चरण 2¹³(2³)³ है। 2¹³/8³ का मान ज्ञात करने के लिए अगला चरण क्या होगा?* 1️⃣ 2¹³⁻³ 2️⃣ 2¹³⁻⁶ 3️⃣ 2¹³⁻⁹ 4️⃣ 2¹³⁺⁹​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The first step to simplify the expression $\displaystyle \sf{ \frac{ {2}^{13} }{ {8}^{3} } }$ is $\displaystyle \sf{ \frac{ {2}^{13} }{ {( {2}^{3} )}^{3} } }$. The next step to simplify the expression $\displaystyle \sf{ \frac{ {2}^{13} }{ {8}^{3} } }$ is

$\displaystyle \sf{ 1. \: \: \: {2}^{13 - 3} }$

$\displaystyle \sf{ 2. \: \: \: {2}^{13 - 6} }$

$\displaystyle \sf{ 3. \: \: \: {2}^{13 - 9} }$

$\displaystyle \sf{ 4. \: \: \: {2}^{13 + 9} }$

CONCEPT TO BE IMPLEMENTED

‌We are aware of the formula on indices that :

‌

‌$\sf{1. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n} }$

‌$\displaystyle \sf{2. \: \: \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }$

‌$\displaystyle \sf{3. \: \: \: { ({a}^{m} )}^{n} = {a}^{mn} }$

‌$\displaystyle \sf{4. \: \: {a}^{0} = 1}$

‌

EVALUATION

Here the given expression is

$\displaystyle \sf{ \frac{ {2}^{13} }{ {8}^{3} } }$

First step

$\displaystyle \sf{ \frac{ {2}^{13} }{ {8}^{3} } }$

$\displaystyle \sf{ = \frac{ {2}^{13} }{ {( {2}^{3} )}^{3} } }$

Second step :

$\displaystyle \sf{ = \frac{ {2}^{13} }{ {8}^{3} } }$

$\displaystyle \sf{ = \frac{ {2}^{13} }{ {( {2}^{3} )}^{3} } }$

$\displaystyle \sf{ = \frac{ {2}^{13} }{ {{2}^{9} }} }$

$\displaystyle \sf{ = {2}^{13 - 9} }$

FINAL ANSWER

Hence the correct option is

$\displaystyle \sf{ 3. \: \: \: {2}^{13 - 9} }$

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