Solve 2^{-4}*3^4*4^-3*5^3*3^5=

$$2 ^ { - 4 } \cdot 3 ^ { 4 } \cdot 4 ^ { - 3 } \cdot 5 ^ { 3 } \cdot 3 ^ { 5 } =$$

Evaluate

$$\frac{2460375}{1024}\approx 2402.709960938$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$2^{-4}\times 3^{9}\times 4^{-3}\times 5^{3}$$

Calculate 2 to the power of -4 and get \frac{1}{16}.

$$\frac{1}{16}\times 3^{9}\times 4^{-3}\times 5^{3}$$

Calculate 3 to the power of 9 and get 19683.

$$\frac{1}{16}\times 19683\times 4^{-3}\times 5^{3}$$

Multiply \frac{1}{16} and 19683 to get \frac{19683}{16}.

$$\frac{19683}{16}\times 4^{-3}\times 5^{3}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{19683}{16}\times \frac{1}{64}\times 5^{3}$$

Multiply \frac{19683}{16} and \frac{1}{64} to get \frac{19683}{1024}.

$$\frac{19683}{1024}\times 5^{3}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{19683}{1024}\times 125$$

Multiply \frac{19683}{1024} and 125 to get \frac{2460375}{1024}.

$$\frac{2460375}{1024}$$

Factor

$$\frac{3 ^ {9} \cdot 5 ^ {3}}{2 ^ {10}} = 2402\frac{727}{1024} = 2402.7099609375$$