Question

find the value of (2/7)^6×7/2^4×2/7^2
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Answer 1

Answer:

2³ / 7⁷

Step-by-step explanation:

2⁶ ÷ 7⁶ * 7 ÷ 2⁴ * 2 ÷ 7²

2⁶⁻⁴⁺¹ * 7⁻⁶⁺¹⁻²

2³ * 7⁻⁷

2³ / 7⁷

Answer 2

Solution :

$\implies \sf { \bigg( \frac{2}{7} \bigg)}^{6} \times {\bigg(\frac{7}{2}\bigg)}^{4} \times {\bigg (\frac{2}{7}\bigg)}^{2} \\ \\ \implies \sf { \bigg( \frac{2}{7} \bigg)}^{6} \div {\bigg(\frac{2}{7}\bigg)}^{4} \times {\bigg (\frac{2}{7}\bigg)}^{2} \\ \\ \implies \sf { \bigg( \frac{2}{7} \bigg)}^{6 - 4} \times {\bigg (\frac{2}{7}\bigg)}^{2} \\ \\ \implies \sf { \bigg( \frac{2}{7} \bigg)}^{2} \times {\bigg (\frac{2}{7}\bigg)}^{2} \\ \\ \implies \sf { \bigg( \frac{2}{7} \bigg)}^{2 + 2} \\ \\ \implies \sf { \bigg( \frac{2}{7} \bigg)}^{4} \\ \\ \implies \sf \frac{16}{2401}$

IdentitY Used :

$\large \implies \sf{m}^{a} \times {m}^{b} = {m}^{a + b} \\ \\ \large \implies \sf{m}^{a} \div {m}^{b} = {m}^{a - b}$