Question

What is the simplified form of the expression k^3(k^7/5)^-5

Answer 1

Step 1. Use the negative power rule:
`x^(-a) = (1)/( x^(a) )`


`k^(3) * (1)/(( ( k^(7) )/(5)) ^(5) )`

Step 2. Use Division Distributive Property:
`( (x)/(y) )^a= (xa)/(ya)`


`k^(3) * 1 ___ (k^(7)) _____ 5^(5)`

Step 3. Use Power Rule:
`( x^(a) )^b=x^a^b`


`k^3*1 ___ k^3^5 _____ 5^5`

Step 4. Simplify
`5^5` to
`3125`


`k^3*1 ___ k^3^5 ______ 3125`

Step 5. Invert and multiply


`k^3*1* (3125)/(k^3^5)`

Step 6. Simplify


`(3125 k^(3) )/(k^3^5)`

Step 7. Use Quotient Rule:
`(xa)/(xb) =x^a^-^b`


`3125k^3^-^3^5`

Step 8. Simplify 3 - 35 to -32


`3125k^-^3^2`

Step 9. Use Negative Power Rule:
`x^-^a= (1)/( x^(a) )`


`3125* (1)/(k^3^2)`

Step 10. Simplify


`(3125)/(k^3^2)`

Done!