Question

[(3/7^4x3/7^5)]divided by (3/7)^7

Answer 1

$\displaystyle \sf{\bigg[ \: {\bigg( \frac{3}{7} \bigg)}^{4} \times {\bigg( \frac{3}{7} \bigg)}^{5} \: \bigg] \div {\bigg( \frac{3}{7} \bigg)}^{7} } = \frac{9}{49}$

Given :

$\displaystyle \sf{\bigg[ \: {\bigg( \frac{3}{7} \bigg)}^{4} \times {\bigg( \frac{3}{7} \bigg)}^{5} \: \bigg] \div {\bigg( \frac{3}{7} \bigg)}^{7} }$

To find :

The value of the expression

Formula :

We are aware of the formula on indices that :

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

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

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{\bigg[ \: {\bigg( \frac{3}{7} \bigg)}^{4} \times {\bigg( \frac{3}{7} \bigg)}^{5} \: \bigg] \div {\bigg( \frac{3}{7} \bigg)}^{7} }$

Step 2 of 2 :

Simplify the given expression

$\displaystyle \sf{\bigg[ \: {\bigg( \frac{3}{7} \bigg)}^{4} \times {\bigg( \frac{3}{7} \bigg)}^{5} \: \bigg] \div {\bigg( \frac{3}{7} \bigg)}^{7} }$

$\displaystyle \sf{ =\bigg[ {\bigg( \frac{3}{7} \bigg)}^{(4 + 5)} \div {\bigg( \frac{3}{7} \bigg)}^{7} }\bigg] \: \: \bigg[ \because \: {a}^{m} \times {a}^{n} = {a}^{m + n} \bigg]$

$\displaystyle \sf{ =\bigg[ {\bigg( \frac{3}{7} \bigg)}^{9} \div {\bigg( \frac{3}{7} \bigg)}^{7} }\bigg]$

$\displaystyle \sf{ = {\bigg( \frac{3}{7} \bigg)}^{9 - 7} \: \: \bigg[ \because \: {a}^{m} \div {a}^{n} = {a}^{m - n} \bigg] }$

$\displaystyle \sf{ = {\bigg( \frac{3}{7} \bigg)}^{2} }$

$\displaystyle \sf{ = \frac{ {3}^{2} }{ {7}^{2} } }$

$\displaystyle \sf{ = \frac{9}{ 49 } }$

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