Question

Simplify (-2/5 raised to power 9*-2/5 raised to power -7)/(-2/5 raised to power 2 ) and express the result as a power of 5​

Answer 1

Answer:

Hi ,

Express 3125 as a product of prime

3125 = 5 × 5 × 5 × 5 × 5 = 5^5

We know that

_________________

1 )( a / b )^ -m = ( b / a ) ^ m

2) a^m / b^m = ( a / b )^ m

__________________

Now ,

( 0.03125 )^ -2/5

=( 3125 /10000 )^-2/5

= ( 10000 / 3125 )^ 2/5

= [ ( 10 )^5 / 5^5 ]^2/5

=[ ( 10 / 5 )^5]^ 2/5

= (2^5 ) ^ 2/5

= 2^( 5/1 × 2/5)

= 2^2

= 4

Therefore ,

( 0.03125 )^ -2/5 = 4

I hope this helps you.

:)