Question

simplify(5/11)6÷(5/11)7​

Answer 1

Step-by-step explanation:

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$( \frac{5}{11} ) 6 \div ( \frac{5}{11} )7 \\ = 42$

Answer 2

$\displaystyle \sf{ { \bigg( \frac{5}{11} \bigg)}^{6} \div { \bigg( \frac{5}{11} \bigg)}^{7} = \frac{11}{5} }$

Given :

$\displaystyle \sf{ { \bigg( \frac{5}{11} \bigg)}^{6} \div { \bigg( \frac{5}{11} \bigg)}^{7} }$

To find :

The value of the expression

Formula :

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

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ { \bigg( \frac{5}{11} \bigg)}^{6} \div { \bigg( \frac{5}{11} \bigg)}^{7} }$

Step 2 of 2 :

Find the value of the expression

We use the formula

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

Thus we get

$\displaystyle \sf{ { \bigg( \frac{5}{11} \bigg)}^{6} \div { \bigg( \frac{5}{11} \bigg)}^{7} }$

$\displaystyle \sf{ = \frac{{ \bigg( \dfrac{5}{11} \bigg)}^{6}}{{ \bigg( \dfrac{5}{11} \bigg)}^{7} } }$

$\displaystyle \sf{ = { \bigg( \dfrac{5}{11} \bigg)}^{6 - 7} }$

$\displaystyle \sf{ = { \bigg( \dfrac{5}{11} \bigg)}^{ - 1} }$

$\displaystyle \sf{ = \frac{1}{ \dfrac{5}{11} } }$

$\displaystyle \sf{ = 1 \times \frac{11}{5} }$

$\displaystyle \sf{ = \frac{11}{5} }$

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