Solve (frac{3^{4}}{3})divfrac{5^{-3}4^-3}{3^-26^22^-2}

$$( \frac { 3 ^ { 4 } } { 3 } ) \div \frac { 5 ^ { - 3 } 4 ^ { - 3 } } { 3 ^ { - 2 } 6 ^ { 2 } 2 ^ { - 2 } }$$

Evaluate

$$216000$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 4 to get 3.

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

Calculate 3 to the power of 3 and get 27.

$$\frac{27}{\frac{5^{-3}\times 4^{-3}}{3^{-2}\times 6^{2}\times 2^{-2}}}$$

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{27}{\frac{\frac{1}{125}\times 4^{-3}}{3^{-2}\times 6^{2}\times 2^{-2}}}$$

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

$$\frac{27}{\frac{\frac{1}{125}\times \frac{1}{64}}{3^{-2}\times 6^{2}\times 2^{-2}}}$$

Multiply \frac{1}{125} and \frac{1}{64} to get \frac{1}{8000}.

$$\frac{27}{\frac{\frac{1}{8000}}{3^{-2}\times 6^{2}\times 2^{-2}}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{27}{\frac{\frac{1}{8000}}{\frac{1}{9}\times 6^{2}\times 2^{-2}}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{27}{\frac{\frac{1}{8000}}{\frac{1}{9}\times 36\times 2^{-2}}}$$

Multiply \frac{1}{9} and 36 to get 4.

$$\frac{27}{\frac{\frac{1}{8000}}{4\times 2^{-2}}}$$

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

$$\frac{27}{\frac{\frac{1}{8000}}{4\times \frac{1}{4}}}$$

Multiply 4 and \frac{1}{4} to get 1.

$$\frac{27}{\frac{\frac{1}{8000}}{1}}$$

Anything divided by one gives itself.

$$\frac{27}{\frac{1}{8000}}$$

Divide 27 by \frac{1}{8000} by multiplying 27 by the reciprocal of \frac{1}{8000}.

$$27\times 8000$$

Multiply 27 and 8000 to get 216000.

$$216000$$

Factor

$$2^{6}\times 3^{3}\times 5^{3}$$