5 raised to 5 all over 3rd root of 5 raised to 7

asked by guest
on Nov 14, 2024 at 5:42 pm



You asked:

Evaluate the expression: \(\frac{{5}^{5}}{\sqrt[3]{{5}^{7}}}\)

MathBot Answer:

\[\frac{{5}^{5}}{\sqrt[3]{{5}^{7}}} = 25 \cdot 5^{\frac{2}{3}} \approx 73.10044345532165163766968400344807\]


\[\begin{aligned}\frac{{5}^{5}}{\sqrt[3]{{5}^{7}}}& = 5^{5} \cdot \frac{1}{\sqrt[3]{5^{7}}}\\& = 3125 \cdot \frac{1}{\sqrt[3]{5^{7}}}\\& = 3125 \cdot \frac{1}{\sqrt[3]{78125}}\\& = 3125 \cdot \frac{1}{25 \cdot \sqrt[3]{5}}\\& = 25 \cdot 5^{\frac{2}{3}}\end{aligned}\]