Question

Simplify and give reasons(4/7)^-5×(7/4)^-7​

Answer 1

Step-by-step explanation:

Answer:

(\frac{4}{7})^{2}(

7

4

)

2

Step-by-step explanation:

Given : (\frac{4}{7})^{-5} \times (\frac{7}{4})^{-7}(

7

4

)

−5

×(

4

7

)

−7

To Find : Simplify

Solution:

(\frac{4}{7})^{-5} \times (\frac{7}{4})^{-7}(

7

4

)

−5

×(

4

7

)

−7

Property: a^{-x}=(\frac{1}{a})^x[/tex So, [tex](\frac{4}{7})^{-5} \times (\frac{4}{7})^{7}a

−x

=(

a

1

)

x

[/texSo, [tex](

7

4

)

−5

×(

7

4

)

7

Property: a^x \times a^y = a^{x+y}a

x

×a

y

=a

x+y

So, (\frac{4}{7})^{-5+7}(

7

4

)

−5+7

(\frac{4}{7})^{2}(

7

4

)

2

Hence (\frac{4}{7})^{-5} \times (\frac{7}{4})^{-7}(

7

4

)

−5

×(

4

7

)

−7

= (\frac{4}{7})^{2}(

7

4

)

2