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

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

Evaluate

$$-\frac{3}{4000}=-0.00075$$

Solution Steps

Calculate 3 to the power of 4 and get 81.

$$\frac{81\times 2^{-2}\times 5^{-3^{1}}}{\left(-6\right)^{3}}$$

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

$$\frac{81\times \frac{1}{4}\times 5^{-3^{1}}}{\left(-6\right)^{3}}$$

Multiply 81 and \frac{1}{4} to get \frac{81}{4}.

$$\frac{\frac{81}{4}\times 5^{-3^{1}}}{\left(-6\right)^{3}}$$

Calculate 3 to the power of 1 and get 3.

$$\frac{\frac{81}{4}\times 5^{-3}}{\left(-6\right)^{3}}$$

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

$$\frac{\frac{81}{4}\times \frac{1}{125}}{\left(-6\right)^{3}}$$

Multiply \frac{81}{4} and \frac{1}{125} to get \frac{81}{500}.

$$\frac{\frac{81}{500}}{\left(-6\right)^{3}}$$

Calculate -6 to the power of 3 and get -216.

$$\frac{\frac{81}{500}}{-216}$$

Express \frac{\frac{81}{500}}{-216} as a single fraction.

$$\frac{81}{500\left(-216\right)}$$

Multiply 500 and -216 to get -108000.

$$\frac{81}{-108000}$$

Reduce the fraction \frac{81}{-108000} to lowest terms by extracting and canceling out 27.

$$-\frac{3}{4000}$$

Factor

$$-\frac{3}{4000} = -0.00075$$