Solve frac{(6x^{3})^{2}}{(2x^2)^3}*(3x^2)^0=

$$\frac { ( 6 x ^ { 3 } ) ^ { 2 } } { ( 2 x ^ { 2 } ) ^ { 3 } } \cdot ( 3 x ^ { 2 } ) ^ { 0 } =$$

Evaluate

$$\frac{9}{2}=4.5$$

Solution Steps

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

$$\frac{6^{2}\left(x^{3}\right)^{2}}{\left(2x^{2}\right)^{3}}\times \left(3x^{2}\right)^{0}$$

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

$$\frac{6^{2}x^{6}}{\left(2x^{2}\right)^{3}}\times \left(3x^{2}\right)^{0}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{36x^{6}}{\left(2x^{2}\right)^{3}}\times \left(3x^{2}\right)^{0}$$

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

$$\frac{36x^{6}}{2^{3}\left(x^{2}\right)^{3}}\times \left(3x^{2}\right)^{0}$$

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

$$\frac{36x^{6}}{2^{3}x^{6}}\times \left(3x^{2}\right)^{0}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{36x^{6}}{8x^{6}}\times \left(3x^{2}\right)^{0}$$

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

$$\frac{9}{2}\times \left(3x^{2}\right)^{0}$$

Calculate 3x^{2} to the power of 0 and get 1.

$$\frac{9}{2}\times 1$$

Multiply \frac{9}{2} and 1 to get \frac{9}{2}.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$