Question

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

Answer 1

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

Answer 2

`\bf a^{( n)/( m)} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{( n)/( m)}\\\\ -------------------------------\\\\ \left( 5^{(4)/(5)} \right)^6\implies 5^{(4)/(5)\cdot 6}\implies 5^{(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}`