(7/8)⁹÷(3/4)⁹
You asked:
Evaluate the expression: \(\frac{{\left( \frac{7}{8} \right)}^{9}}{{\left( \frac{3}{4} \right)}^{9}}\)
MathBot Answer:
\[\frac{{\left( \frac{7}{8} \right)}^{9}}{{\left( \frac{3}{4} \right)}^{9}} = \frac{40353607}{10077696} \approx 4.00424928475715084082710968856374\]
\[\begin{aligned}\frac{{\left( \frac{7}{8} \right)}^{9}}{{\left( \frac{3}{4} \right)}^{9}}& = \left(\frac{7}{8}\right)^{9} \cdot \frac{1}{\left(\frac{3}{4}\right)^{9}}\\& = \frac{40353607}{134217728} \cdot \frac{1}{\left(\frac{3}{4}\right)^{9}}\\& = \frac{40353607}{134217728} \cdot \frac{1}{\frac{19683}{262144}}\\& = \frac{40353607}{10077696}\end{aligned}\]