Solve (4x^4)^2div8(x^3)^2

$$( 4 x ^ { 4 } ) ^ { 2 } \div 8 ( x ^ { 3 } ) ^ { 2 }$$

Evaluate

$$2x^{14}$$

Solution Steps

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

$$\frac{\left(4x^{4}\right)^{2}}{8}x^{6}$$

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

$$\frac{4^{2}\left(x^{4}\right)^{2}}{8}x^{6}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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

Calculate 4 to the power of 2 and get 16.

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

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

$$2x^{8}x^{6}$$

To multiply powers of the same base, add their exponents. Add 8 and 6 to get 14.

$$2x^{14}$$

Expand

$$2x^{14}$$

Solution Steps

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

$$\frac{\left(4x^{4}\right)^{2}}{8}x^{6}$$

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

$$\frac{4^{2}\left(x^{4}\right)^{2}}{8}x^{6}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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

Calculate 4 to the power of 2 and get 16.

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

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

$$2x^{8}x^{6}$$

To multiply powers of the same base, add their exponents. Add 8 and 6 to get 14.

$$2x^{14}$$