Solve frac{(3^{3})^{-2}*(2^{2})^{-3}}{(2^4)^-2*3^-4*4^-2}

$$\frac { ( 3 ^ { 3 } ) ^ { - 2 } \times ( 2 ^ { 2 } ) ^ { - 3 } } { ( 2 ^ { 4 } ) ^ { - 2 } \times 3 ^ { - 4 } \times 4 ^ { - 2 } }$$

Evaluate

$$\frac{64}{9}\approx 7.111111111$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$\frac{3^{-6}\times \left(2^{2}\right)^{-3}}{\left(2^{4}\right)^{-2}\times 3^{-4}\times 4^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -3 to get -6.

$$\frac{3^{-6}\times 2^{-6}}{\left(2^{4}\right)^{-2}\times 3^{-4}\times 4^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{3^{-6}\times 2^{-6}}{2^{-8}\times 3^{-4}\times 4^{-2}}$$

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Calculate 3 to the power of 2 and get 9.

$$\frac{4}{9\times 4^{-2}}$$

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

$$\frac{4}{9\times \frac{1}{16}}$$

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

$$\frac{4}{\frac{9}{16}}$$

Divide 4 by \frac{9}{16} by multiplying 4 by the reciprocal of \frac{9}{16}.

$$4\times \frac{16}{9}$$

Multiply 4 and \frac{16}{9} to get \frac{64}{9}.

$$\frac{64}{9}$$

Factor

$$\frac{2 ^ {6}}{3 ^ {2}} = 7\frac{1}{9} = 7.111111111111111$$