Question

find the value of 7² ÷ 7⁵​

Answer 1

Step-by-step explanation:

1/343 is the answer

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Answer 2

SOLUTION

TO DETERMINE

The value of 7² ÷ 7⁵

FORMULA TO BE IMPLEMENTED

We are aware of the formula on indices that

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

EVALUATION

Here the given expression is 7² ÷ 7⁵

Now we apply the formula

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

$\sf {7}^{2} \div {7}^{5}$

$\displaystyle \sf{ =\frac{ {7}^{2} }{ {7}^{5} } }$

$\displaystyle \sf{ = {7}^{2 - 5} }$

$\displaystyle \sf{ = {7}^{-3} }$

$\displaystyle \sf{ = \frac{1}{ {7}^{3} } }$

$\displaystyle \sf{ = \frac{1}{ 7 \times 7 \times 7 } }$

$\displaystyle \sf{ = \frac{1}{ 343} }$

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