Question

What is the value of 5 to the power of 4 over 5 to the power of 6?

Answer 1

$\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\ -------------------------------\\\\ \left( 5^{\frac{4}{5}} \right)^6\implies 5^{\frac{4}{5}\cdot 6}\implies 5^{\frac{24}{5}}\implies \sqrt[5]{5^{24}}~~ \begin{cases} 5^{24}=5^{5+5+5+5+4}\\ \qquad 5^5\cdot 5^5\cdot 5^5\cdot 5^5\cdot 5^4\\ \qquad (5^4)^5 5^4 \end{cases} \\\\\\ \sqrt[5]{(5^4)^5 \cdot 5^4}\implies (5^4)\sqrt[5]{5^4}\implies 625\sqrt[5]{625}$

Answer 2

If the question is 5^4 divided by 5^6 the asnwer is .04