Solve (7/8)^9:(3/4)^9

$$( \frac { 7 } { 8 } ) ^ { 9 } : ( \frac { 3 } { 4 } ) ^ { 9 }$$

Evaluate

$$\frac{40353607}{10077696}\approx 4.004249285$$

Solution Steps

Calculate \frac{7}{8} to the power of 9 and get \frac{40353607}{134217728}.

$$\frac{\frac{40353607}{134217728}}{\left(\frac{3}{4}\right)^{9}}$$

Calculate \frac{3}{4} to the power of 9 and get \frac{19683}{262144}.

$$\frac{\frac{40353607}{134217728}}{\frac{19683}{262144}}$$

Divide \frac{40353607}{134217728} by \frac{19683}{262144} by multiplying \frac{40353607}{134217728} by the reciprocal of \frac{19683}{262144}.

$$\frac{40353607}{134217728}\times \frac{262144}{19683}$$

Multiply \frac{40353607}{134217728} times \frac{262144}{19683} by multiplying numerator times numerator and denominator times denominator.

$$\frac{40353607\times 262144}{134217728\times 19683}$$

Do the multiplications in the fraction \frac{40353607\times 262144}{134217728\times 19683}.

$$\frac{10578455953408}{2641807540224}$$

Reduce the fraction \frac{10578455953408}{2641807540224} to lowest terms by extracting and canceling out 262144.

$$\frac{40353607}{10077696}$$

Factor

$$\frac{7 ^ {9}}{2 ^ {9} \cdot 3 ^ {9}} = 4\frac{42823}{10077696} = 4.004249284757151$$