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