Solve (frac{(6x^{3})^{2}}{(2x^2)^3})(3x^2)^5

$$( \frac { ( 6 x ^ { 3 } ) ^ { 2 } } { ( 2 x ^ { 2 } ) ^ { 3 } } ) ( 3 x ^ { 2 } ) ^ { 5 }$$

Evaluate

$$\frac{2187x^{10}}{2}$$

Solution Steps

Expand \left(6x^{3}\right)^{2}.

$$\frac{6^{2}\left(x^{3}\right)^{2}}{\left(2x^{2}\right)^{3}}\times \left(3x^{2}\right)^{5}$$

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

$$\frac{6^{2}x^{6}}{\left(2x^{2}\right)^{3}}\times \left(3x^{2}\right)^{5}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{36x^{6}}{\left(2x^{2}\right)^{3}}\times \left(3x^{2}\right)^{5}$$

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

$$\frac{36x^{6}}{2^{3}\left(x^{2}\right)^{3}}\times \left(3x^{2}\right)^{5}$$

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

$$\frac{36x^{6}}{2^{3}x^{6}}\times \left(3x^{2}\right)^{5}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{36x^{6}}{8x^{6}}\times \left(3x^{2}\right)^{5}$$

Cancel out 4x^{6} in both numerator and denominator.

$$\frac{9}{2}\times \left(3x^{2}\right)^{5}$$

Expand \left(3x^{2}\right)^{5}.

$$\frac{9}{2}\times 3^{5}\left(x^{2}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{9}{2}\times 3^{5}x^{10}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{9}{2}\times 243x^{10}$$

Multiply \frac{9}{2} and 243 to get \frac{2187}{2}.

$$\frac{2187}{2}x^{10}$$

Expand

$$\frac{2187x^{10}}{2}$$

Solution Steps

Expand \left(6x^{3}\right)^{2}.

$$\frac{6^{2}\left(x^{3}\right)^{2}}{\left(2x^{2}\right)^{3}}\times \left(3x^{2}\right)^{5}$$

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

$$\frac{6^{2}x^{6}}{\left(2x^{2}\right)^{3}}\times \left(3x^{2}\right)^{5}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{36x^{6}}{\left(2x^{2}\right)^{3}}\times \left(3x^{2}\right)^{5}$$

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

$$\frac{36x^{6}}{2^{3}\left(x^{2}\right)^{3}}\times \left(3x^{2}\right)^{5}$$

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

$$\frac{36x^{6}}{2^{3}x^{6}}\times \left(3x^{2}\right)^{5}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{36x^{6}}{8x^{6}}\times \left(3x^{2}\right)^{5}$$

Cancel out 4x^{6} in both numerator and denominator.

$$\frac{9}{2}\times \left(3x^{2}\right)^{5}$$

Expand \left(3x^{2}\right)^{5}.

$$\frac{9}{2}\times 3^{5}\left(x^{2}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{9}{2}\times 3^{5}x^{10}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{9}{2}\times 243x^{10}$$

Multiply \frac{9}{2} and 243 to get \frac{2187}{2}.

$$\frac{2187}{2}x^{10}$$