Question

find the value of (7/5)¹ ÷ (5/7)²​

Answer 1

Answer:

Step-by-step explanation:

Given that,

(7/5) ÷ (5/7)²

= 7/5 × (7/5)²

= (7/5) power (1 + 2) ( ∵Bases are equal then power's should be add )

= (7/5)³

Answer 2

Answer:

$\frac{343}{125}$

Step-by-step explanation:

• Given: $(\frac{7}{5})^{1}\div (\frac{5}{7})^{2}$

• As we know that $(\frac{a}{b})^{n} =\frac{a^{n} }{b^{n} }$ and $a^{1}=a$

• By applying above formula in the given expression, we get

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

$=\frac{7}{5}\div \frac{25}{49}$

• To divide a fraction with another fraction, multiply that fraction by the reciprocal of the second fraction.

• Reciprocal of $\frac{25}{49} =\frac{49}{25}$

$=\frac{7}{5} \times \frac{49}{25}$

$=\frac{343}{125}$

Hence, the value of $(\frac{7}{5})^{1}\div (\frac{5}{7})^{2}$ is $\frac{343}{125}$.