Solve (49/9)^18:(29/9)^15

$$( \frac { 49 } { 9 } ) ^ { 18 } : ( \frac { 29 } { 9 } ) ^ { 15 }$$

Evaluate

$$\frac{2651730845859653471779023381601}{6290678596999076457451821}\approx 421533.35367104$$

Solution Steps

Calculate \frac{49}{9} to the power of 18 and get \frac{2651730845859653471779023381601}{150094635296999121}.

$$\frac{\frac{2651730845859653471779023381601}{150094635296999121}}{\left(\frac{29}{9}\right)^{15}}$$

Calculate \frac{29}{9} to the power of 15 and get \frac{8629188747598184440949}{205891132094649}.

$$\frac{\frac{2651730845859653471779023381601}{150094635296999121}}{\frac{8629188747598184440949}{205891132094649}}$$

Divide \frac{2651730845859653471779023381601}{150094635296999121} by \frac{8629188747598184440949}{205891132094649} by multiplying \frac{2651730845859653471779023381601}{150094635296999121} by the reciprocal of \frac{8629188747598184440949}{205891132094649}.

$$\frac{2651730845859653471779023381601}{150094635296999121}\times \frac{205891132094649}{8629188747598184440949}$$

Multiply \frac{2651730845859653471779023381601}{150094635296999121} times \frac{205891132094649}{8629188747598184440949} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2651730845859653471779023381601\times 205891132094649}{150094635296999121\times 8629188747598184440949}$$

Do the multiplications in the fraction \frac{2651730845859653471779023381601\times 205891132094649}{150094635296999121\times 8629188747598184440949}.

$$\frac{545967865864345239262083519342710646377153049}{1295194937979718093306670848772729405829}$$

Reduce the fraction \frac{545967865864345239262083519342710646377153049}{1295194937979718093306670848772729405829} to lowest terms by extracting and canceling out 205891132094649.

$$\frac{2651730845859653471779023381601}{6290678596999076457451821}$$

Factor

$$\frac{7 ^ {36}}{3 ^ {6} \cdot 29 ^ {15}} = 421533\frac{2.224830841937589 \times 10^{24}}{6.290678596999077 \times 10^{24}} = 421533.35367104004$$