Question

Evaluate :
3 power -7 ÷ 3 power -10×3 power -5​

Answer 1

SOLUTION

TO EVALUATE

$\displaystyle \sf{ \frac{ {3}^{ - 7} }{ {3}^{ - 10} \times {3}^{ - 5} } }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on indices that

$\displaystyle \sf{1. \: \: {a}^{m} \div {a}^{n} = {a}^{m - n} }$

$\displaystyle \sf{2. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n} }$

EVALUATION

$\displaystyle \sf{ \frac{ {3}^{ - 7} }{ {3}^{ - 10} \times {3}^{ - 5} } }$

$\displaystyle \sf{ = \frac{ {3}^{ - 7} }{ {3}^{ - 10 - 5} }}$

$\displaystyle \sf{ = \frac{ {3}^{ - 7} }{ {3}^{ - 1 5} }}$

$\displaystyle \sf{ = {3}^{ - 7 + 15}}$

$\displaystyle \sf{ = {3}^{8}}$

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