Question

simplify these questions ​

Answer 1

Answer:

$\tt{ (\dfrac{5}{7})^{3} \times (\dfrac{5}{7})^{-5} = \dfrac{49}{25} }$

Step-by-step explanation:

Given: $\tt{ (\dfrac{5}{7})^{3} \times (\dfrac{5}{7})^{-5} }$

$\tt{ = (\dfrac{5}{7})^{3} \times (\dfrac{7}{5})^{5} }$

$\tt{ = \dfrac{5^{3}}{7^{3}} \times \dfrac{7^{5}}{5^{5}} }$

$\tt{ = 5^{3-5} \times 7^{5-3} }$

$\tt{ = 5^{-2} \times 7^{2} }$

$\tt{ = \dfrac{7^{2}}{5^{2}} }$

= 49/25

Formulas used (Laws of Exponent) :-

1) a⁻ⁿ = 1/aⁿ

2) aⁿ × aˣ = aⁿ⁺ˣ

3) aⁿ/aˣ = aⁿ⁻ˣ