Solve (4x^3)^2(2x^4)/16x^3

$$\frac { ( 4 x ^ { 3 } ) ^ { 2 } ( 2 x ^ { 4 } ) } { 16 x ^ { 3 } }$$

Evaluate

$$2x^{7}$$

Solution Steps

Cancel out 2x^{3} in both numerator and denominator.

$$\frac{x\times \left(4x^{3}\right)^{2}}{8}$$

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

$$\frac{x\times 4^{2}\left(x^{3}\right)^{2}}{8}$$

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

$$\frac{x\times 4^{2}x^{6}}{8}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{x\times 16x^{6}}{8}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{x^{7}\times 16}{8}$$

Divide x^{7}\times 16 by 8 to get x^{7}\times 2.

$$x^{7}\times 2$$

Expand

$$2x^{7}$$

Solution Steps

Cancel out 2x^{3} in both numerator and denominator.

$$\frac{x\times \left(4x^{3}\right)^{2}}{8}$$

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

$$\frac{x\times 4^{2}\left(x^{3}\right)^{2}}{8}$$

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

$$\frac{x\times 4^{2}x^{6}}{8}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{x\times 16x^{6}}{8}$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{x^{7}\times 16}{8}$$

Divide x^{7}\times 16 by 8 to get x^{7}\times 2.

$$x^{7}\times 2$$