Question

(ii) simplify
[12^1/5\27 ^1/5 ]5\2​

Answer 1

Answer:

The answer is 2/3.

Step-by-step explanation:

Here, the given expression,

(\frac{12^\frac{1}{5}}{27^\frac{1}{5}})^\frac{5}{2}(

27

5

1

12

5

1

)

2

5

=\frac{(12^\frac{1}{5})^\frac{5}{2}}{(27^\frac{1}{5})^\frac{5}{2}}=

(27

5

1

)

2

5

(12

5

1

)

2

5

=\frac{12^{\frac{1}{5}\times \frac{5}{2}}}{27^{\frac{1}{5}\times \frac{5}{2}}}=

27

5

1

×

2

5

12

5

1

×

2

5

=\frac{12^\frac{1}{2}}{27^\frac{1}{2}}=

27

2

1

12

2

1

=(\frac{12}{27})^\frac{1}{2}=(

27

12

)

2

1

=(\frac{4}{9})^\frac{1}{2}=(

9

4

)

2

1

=\sqrt{\frac{4}{9}}=

9

4

=\frac{2}{3}=

3

2