Question

Help me solve this problem

Evaluate....

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Answer 1

The answer is 49

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Answer 2

Evaluate :-

$\sf{ \dfrac{({7}^{4})^{2} \times {(7)}^{ - 2}}{ {7}^{4}}}$

Answer :

The required number is 49.

Step-by-step explanation ::

$\sf{ \mapsto \: \dfrac{({7}^{4})^{2} \times {(7)}^{ - 2}}{{7}^{4}}} \\ \\ \\ \sf{ \mapsto \: \dfrac{(2401)^{2} \times {(7)}^{ - 2}}{{7}^{4}}} \\ \\ \\ \sf{ \mapsto \: \dfrac{5764801 \times {(7)}^{ - 2}}{{7}^{4}}} \\ \\ \\ \sf{ \mapsto \: \dfrac{5764801 \times { \dfrac{1}{49}}}{{7}^{4}}} \\ \\ \\ \sf{ \mapsto \: \dfrac{ \cancel{5764801} \times { \dfrac{1}{ \cancel{49}}}}{{7}^{4}}} \\ \\ \\ \sf{ \mapsto \: \dfrac{117649}{{7}^{4}}} \\ \\ \\ \sf{ \mapsto \: \dfrac{117649}{2401}} \\ \\ \\ \sf{\mapsto \: \cancel{\dfrac{117649}{2401}}} \\ \\ \\ \bf{ \mapsto \: 49 \: \: \dag}$

The required number is 49.

Now, VerificatioN

$\sf{ \mapsto \: \dfrac{({7}^{4})^{2} \times {(7)}^{ - 2}}{{7}^{4}} = 49} \\ \\ \\ \sf{ \mapsto \: \dfrac{(2401)^{2} \times {(7)}^{ - 2}}{{7}^{4}} = 49} \\ \\ \\ \sf{ \mapsto \: \dfrac{5764801 \times {(7)}^{ - 2}}{{7}^{4}} = 49} \\ \\ \\ \sf{ \mapsto \: \dfrac{5764801 \times { \dfrac{1}{49}}}{{7}^{4}} = 49} \\ \\ \\ \sf{ \mapsto \: \dfrac{ \cancel{5764801} \times { \dfrac{1}{ \cancel{49}}}}{{7}^{4}} = 49} \\ \\ \\ \sf{ \mapsto \: \dfrac{117649}{{7}^{4}} = 49} \\ \\ \\ \sf{ \mapsto \: \dfrac{117649}{2401} = 49} \\ \\ \\ \sf{\mapsto \: \cancel{\dfrac{117649}{2401}} = 49} \\ \\ \\ \bf{ \mapsto \: 49 = 49\: \: \dag}$

L.H.S = R.H.S

Hence, Verified !