Solve frac{(3rs^{2}t^{2})^2}{21r^2s^3t^11}

$$\frac { ( 3 r s ^ { 2 } t ^ { 2 } ) ^ { 2 } } { 21 r ^ { 2 } s ^ { 3 } t ^ { 11 } }$$

Evaluate

$$\frac{3s}{7t^{7}}$$

Solution Steps

Expand \left(3rs^{2}t^{2}\right)^{2}.

$$\frac{3^{2}r^{2}\left(s^{2}\right)^{2}\left(t^{2}\right)^{2}}{21r^{2}s^{3}t^{11}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{3^{2}r^{2}s^{4}\left(t^{2}\right)^{2}}{21r^{2}s^{3}t^{11}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{3^{2}r^{2}s^{4}t^{4}}{21r^{2}s^{3}t^{11}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9r^{2}s^{4}t^{4}}{21r^{2}s^{3}t^{11}}$$

Cancel out 3r^{2}s^{3}t^{4} in both numerator and denominator.

$$\frac{3s}{7t^{7}}$$

Expand

$$\frac{3s}{7t^{7}}$$

Solution Steps

Expand \left(3rs^{2}t^{2}\right)^{2}.

$$\frac{3^{2}r^{2}\left(s^{2}\right)^{2}\left(t^{2}\right)^{2}}{21r^{2}s^{3}t^{11}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{3^{2}r^{2}s^{4}\left(t^{2}\right)^{2}}{21r^{2}s^{3}t^{11}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{3^{2}r^{2}s^{4}t^{4}}{21r^{2}s^{3}t^{11}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9r^{2}s^{4}t^{4}}{21r^{2}s^{3}t^{11}}$$

Cancel out 3r^{2}s^{3}t^{4} in both numerator and denominator.

$$\frac{3s}{7t^{7}}$$