Step 1. Use the negative power rule: [tex] x^{-a} = \frac{1}{ x^{a} } [/tex]
[tex] k^{3} * \frac{1}{( \frac{ k^{7} }{5}) ^{5} }[/tex]
Step 2. Use Division Distributive Property: [tex]( \frac{x}{y} )^a= \frac{xa}{ya} [/tex]
[tex] k^{3} * 1
___
(k^{7})
_____
5^{5} [/tex]
Step 3. Use Power Rule: [tex]( x^{a} )^b=x^a^b[/tex]
[tex]k^3*1
___
k^3^5
_____
5^5[/tex]
Step 4. Simplify [tex]5^5[/tex] to [tex]3125[/tex]
[tex]k^3*1
___
k^3^5
______
3125[/tex]
Step 5. Invert and multiply
[tex]k^3*1* \frac{3125}{k^3^5} [/tex]
Step 6. Simplify
[tex] \frac{3125 k^{3} }{k^3^5} [/tex]
Step 7. Use Quotient Rule: [tex] \frac{xa}{xb} =x^a^-^b[/tex]
[tex]3125k^3^-^3^5[/tex]
Step 8. Simplify 3 - 35 to -32
[tex]3125k^-^3^2[/tex]
Step 9. Use Negative Power Rule: [tex]x^-^a= \frac{1}{ x^{a} } [/tex]
[tex]3125* \frac{1}{k^3^2} [/tex]
Step 10. Simplify
[tex] \frac{3125}{k^3^2} [/tex]
Done!
