Solve frac{(3n^{3}f^4)^3}{1n^7f^30}

$$\frac { ( 3 n ^ { 3 } f ^ { 4 } ) ^ { 3 } } { 1 n ^ { 7 } f ^ { 30 } }$$

Evaluate

$$\frac{27n^{2}}{f^{18}}$$

Solution Steps

Expand \left(3n^{3}f^{4}\right)^{3}.

$$\frac{3^{3}\left(n^{3}\right)^{3}\left(f^{4}\right)^{3}}{1n^{7}f^{30}}$$

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

$$\frac{3^{3}n^{9}\left(f^{4}\right)^{3}}{1n^{7}f^{30}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{3^{3}n^{9}f^{12}}{1n^{7}f^{30}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27n^{9}f^{12}}{1n^{7}f^{30}}$$

Cancel out n^{7}f^{12} in both numerator and denominator.

$$\frac{27n^{2}}{f^{18}}$$

Expand

$$\frac{27n^{2}}{f^{18}}$$

Solution Steps

Expand \left(3n^{3}f^{4}\right)^{3}.

$$\frac{3^{3}\left(n^{3}\right)^{3}\left(f^{4}\right)^{3}}{1n^{7}f^{30}}$$

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

$$\frac{3^{3}n^{9}\left(f^{4}\right)^{3}}{1n^{7}f^{30}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{3^{3}n^{9}f^{12}}{1n^{7}f^{30}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27n^{9}f^{12}}{1n^{7}f^{30}}$$

Cancel out n^{7}f^{12} in both numerator and denominator.

$$\frac{27n^{2}}{f^{18}}$$