Solve frac{5^{-3}*2^4*4^-2}{6^-3*2^-3*5}

$$\frac { 5 ^ { - 3 } \times 2 ^ { 4 } \times 4 ^ { - 2 } } { 6 ^ { - 3 } \times 2 ^ { - 3 } \times 5 }$$

Evaluate

$$\frac{1728}{625}=2.7648$$

Solution Steps

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

$$\frac{2^{7}\times 4^{-2}\times 5^{-3}}{5\times 6^{-3}}$$

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

$$\frac{2^{7}\times 4^{-2}}{5^{4}\times 6^{-3}}$$

Calculate 2 to the power of 7 and get 128.

$$\frac{128\times 4^{-2}}{5^{4}\times 6^{-3}}$$

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

$$\frac{128\times \frac{1}{16}}{5^{4}\times 6^{-3}}$$

Multiply 128 and \frac{1}{16} to get 8.

$$\frac{8}{5^{4}\times 6^{-3}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{8}{625\times 6^{-3}}$$

Calculate 6 to the power of -3 and get \frac{1}{216}.

$$\frac{8}{625\times \frac{1}{216}}$$

Multiply 625 and \frac{1}{216} to get \frac{625}{216}.

$$\frac{8}{\frac{625}{216}}$$

Divide 8 by \frac{625}{216} by multiplying 8 by the reciprocal of \frac{625}{216}.

$$8\times \frac{216}{625}$$

Multiply 8 and \frac{216}{625} to get \frac{1728}{625}.

$$\frac{1728}{625}$$

Factor

$$\frac{2 ^ {6} \cdot 3 ^ {3}}{5 ^ {4}} = 2\frac{478}{625} = 2.7648$$