Solve (4x^3/3x^6)^-3

$$( \frac { 4 x ^ { 3 } } { 3 x ^ { 6 } } ) ^ { - 3 }$$

Evaluate

$$\frac{27x^{9}}{64}$$

Solution Steps

Cancel out x^{3} in both numerator and denominator.

$$\left(\frac{4}{3x^{3}}\right)^{-3}$$

To raise \frac{4}{3x^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{4^{-3}}{\left(3x^{3}\right)^{-3}}$$

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

$$\frac{\frac{1}{64}}{\left(3x^{3}\right)^{-3}}$$

Expand \left(3x^{3}\right)^{-3}.

$$\frac{\frac{1}{64}}{3^{-3}\left(x^{3}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -3 to get -9.

$$\frac{\frac{1}{64}}{3^{-3}x^{-9}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{\frac{1}{64}}{\frac{1}{27}x^{-9}}$$

Express \frac{\frac{1}{64}}{\frac{1}{27}x^{-9}} as a single fraction.

$$\frac{1}{64\times \frac{1}{27}x^{-9}}$$

Multiply 64 and \frac{1}{27} to get \frac{64}{27}.

$$\frac{1}{\frac{64}{27}x^{-9}}$$

Expand

$$\frac{27x^{9}}{64}$$

Solution Steps

Cancel out x^{3} in both numerator and denominator.

$$\left(\frac{4}{3x^{3}}\right)^{-3}$$

To raise \frac{4}{3x^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{4^{-3}}{\left(3x^{3}\right)^{-3}}$$

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

$$\frac{\frac{1}{64}}{\left(3x^{3}\right)^{-3}}$$

Expand \left(3x^{3}\right)^{-3}.

$$\frac{\frac{1}{64}}{3^{-3}\left(x^{3}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -3 to get -9.

$$\frac{\frac{1}{64}}{3^{-3}x^{-9}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{\frac{1}{64}}{\frac{1}{27}x^{-9}}$$

Express \frac{\frac{1}{64}}{\frac{1}{27}x^{-9}} as a single fraction.

$$\frac{1}{64\times \frac{1}{27}x^{-9}}$$

Multiply 64 and \frac{1}{27} to get \frac{64}{27}.

$$\frac{1}{\frac{64}{27}x^{-9}}$$