Solve (4x^2)^3/(3x^6)^2

$$\frac { ( 4 x ^ { 2 } ) ^ { 3 } } { ( 3 x ^ { 6 } ) ^ { 2 } }$$

Evaluate

$$\frac{64}{9x^{6}}$$

Solution Steps

Expand \left(4x^{2}\right)^{3}.

$$\frac{4^{3}\left(x^{2}\right)^{3}}{\left(3x^{6}\right)^{2}}$$

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

$$\frac{4^{3}x^{6}}{\left(3x^{6}\right)^{2}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64x^{6}}{\left(3x^{6}\right)^{2}}$$

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

$$\frac{64x^{6}}{3^{2}\left(x^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{64x^{6}}{3^{2}x^{12}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{64x^{6}}{9x^{12}}$$

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

$$\frac{64}{9x^{6}}$$

Expand

$$\frac{64}{9x^{6}}$$

Solution Steps

Expand \left(4x^{2}\right)^{3}.

$$\frac{4^{3}\left(x^{2}\right)^{3}}{\left(3x^{6}\right)^{2}}$$

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

$$\frac{4^{3}x^{6}}{\left(3x^{6}\right)^{2}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64x^{6}}{\left(3x^{6}\right)^{2}}$$

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

$$\frac{64x^{6}}{3^{2}\left(x^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{64x^{6}}{3^{2}x^{12}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{64x^{6}}{9x^{12}}$$

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

$$\frac{64}{9x^{6}}$$