Solve (frac{-5e^{5}f^{6}g^-2}{3e^8g^-4})^3

$$( \frac { - 5 e ^ { 5 } f ^ { 6 } g ^ { - 2 } } { 3 e ^ { 8 } g ^ { - 4 } } ) ^ { 3 }$$

Evaluate

$$-\frac{125g^{6}f^{18}}{27e^{9}}$$

Solution Steps

Cancel out e^{5} in both numerator and denominator.

$$\left(\frac{-5g^{-2}f^{6}}{3e^{3}g^{-4}}\right)^{3}$$

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

$$\left(\frac{-5g^{2}f^{6}}{3e^{3}}\right)^{3}$$

To raise \frac{-5g^{2}f^{6}}{3e^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-5g^{2}f^{6}\right)^{3}}{\left(3e^{3}\right)^{3}}$$

Expand \left(-5g^{2}f^{6}\right)^{3}.

$$\frac{\left(-5\right)^{3}\left(g^{2}\right)^{3}\left(f^{6}\right)^{3}}{\left(3e^{3}\right)^{3}}$$

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

$$\frac{\left(-5\right)^{3}g^{6}\left(f^{6}\right)^{3}}{\left(3e^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{\left(-5\right)^{3}g^{6}f^{18}}{\left(3e^{3}\right)^{3}}$$

Calculate -5 to the power of 3 and get -125.

$$\frac{-125g^{6}f^{18}}{\left(3e^{3}\right)^{3}}$$

Expand \left(3e^{3}\right)^{3}.

$$\frac{-125g^{6}f^{18}}{3^{3}\left(e^{3}\right)^{3}}$$

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

$$\frac{-125g^{6}f^{18}}{3^{3}e^{9}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{-125g^{6}f^{18}}{27e^{9}}$$

Expand

$$-\frac{125g^{6}f^{18}}{27e^{9}}$$

Solution Steps

Cancel out e^{5} in both numerator and denominator.

$$\left(\frac{-5g^{-2}f^{6}}{3e^{3}g^{-4}}\right)^{3}$$

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

$$\left(\frac{-5g^{2}f^{6}}{3e^{3}}\right)^{3}$$

To raise \frac{-5g^{2}f^{6}}{3e^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-5g^{2}f^{6}\right)^{3}}{\left(3e^{3}\right)^{3}}$$

Expand \left(-5g^{2}f^{6}\right)^{3}.

$$\frac{\left(-5\right)^{3}\left(g^{2}\right)^{3}\left(f^{6}\right)^{3}}{\left(3e^{3}\right)^{3}}$$

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

$$\frac{\left(-5\right)^{3}g^{6}\left(f^{6}\right)^{3}}{\left(3e^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{\left(-5\right)^{3}g^{6}f^{18}}{\left(3e^{3}\right)^{3}}$$

Calculate -5 to the power of 3 and get -125.

$$\frac{-125g^{6}f^{18}}{\left(3e^{3}\right)^{3}}$$

Expand \left(3e^{3}\right)^{3}.

$$\frac{-125g^{6}f^{18}}{3^{3}\left(e^{3}\right)^{3}}$$

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

$$\frac{-125g^{6}f^{18}}{3^{3}e^{9}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{-125g^{6}f^{18}}{27e^{9}}$$