Solve (4h^3*hk^4)^2/2h^5k

$$\frac { ( 4 h ^ { 3 } \times h k ^ { 4 } ) ^ { 2 } } { 2 h ^ { 5 } k }$$

Evaluate

$$8h^{3}k^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\left(4h^{4}k^{4}\right)^{2}}{2h^{5}k}$$

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

$$\frac{4^{2}\left(h^{4}\right)^{2}\left(k^{4}\right)^{2}}{2h^{5}k}$$

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

$$\frac{4^{2}h^{8}\left(k^{4}\right)^{2}}{2h^{5}k}$$

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

$$\frac{4^{2}h^{8}k^{8}}{2h^{5}k}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16h^{8}k^{8}}{2h^{5}k}$$

Cancel out 2kh^{5} in both numerator and denominator.

$$8h^{3}k^{7}$$

Expand

$$8h^{3}k^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\left(4h^{4}k^{4}\right)^{2}}{2h^{5}k}$$

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

$$\frac{4^{2}\left(h^{4}\right)^{2}\left(k^{4}\right)^{2}}{2h^{5}k}$$

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

$$\frac{4^{2}h^{8}\left(k^{4}\right)^{2}}{2h^{5}k}$$

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

$$\frac{4^{2}h^{8}k^{8}}{2h^{5}k}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16h^{8}k^{8}}{2h^{5}k}$$

Cancel out 2kh^{5} in both numerator and denominator.

$$8h^{3}k^{7}$$