Solve frac{3^{-4}*16*9^-1}{8^2*3^-5*2^-3}=

$$\frac { 3 ^ { - 4 } \cdot 16 \cdot 9 ^ { - 1 } } { 8 ^ { 2 } \cdot 3 ^ { - 5 } \cdot 2 ^ { - 3 } } =$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{16\times 3^{1}\times \frac{1}{9}}{2^{-3}\times 8^{2}}$$

Calculate 3 to the power of 1 and get 3.

$$\frac{16\times 3\times \frac{1}{9}}{2^{-3}\times 8^{2}}$$

Multiply 16 and 3 to get 48.

$$\frac{48\times \frac{1}{9}}{2^{-3}\times 8^{2}}$$

Multiply 48 and \frac{1}{9} to get \frac{16}{3}.

$$\frac{\frac{16}{3}}{2^{-3}\times 8^{2}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{16}{3}}{\frac{1}{8}\times 8^{2}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{\frac{16}{3}}{\frac{1}{8}\times 64}$$

Multiply \frac{1}{8} and 64 to get 8.

$$\frac{\frac{16}{3}}{8}$$

Express \frac{\frac{16}{3}}{8} as a single fraction.

$$\frac{16}{3\times 8}$$

Multiply 3 and 8 to get 24.

$$\frac{16}{24}$$

Reduce the fraction \frac{16}{24} to lowest terms by extracting and canceling out 8.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$