Solve (frac{m^{5/2}(2m^5/4)^2}{m^1/2})^2

$$( \frac { m ^ { 5 / 2 } ( 2 m ^ { 5 / 4 } ) ^ { 2 } } { m ^ { 1 / 2 } } ) ^ { 2 }$$

Evaluate

$$16m^{9}$$

Solution Steps

Cancel out \sqrt{m} in both numerator and denominator.

$$\left(m^{2}\times \left(2m^{\frac{5}{4}}\right)^{2}\right)^{2}$$

Expand \left(m^{2}\times \left(2m^{\frac{5}{4}}\right)^{2}\right)^{2}.

$$\left(m^{2}\right)^{2}\times \left(\left(2m^{\frac{5}{4}}\right)^{2}\right)^{2}$$

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

$$m^{4}\times \left(\left(2m^{\frac{5}{4}}\right)^{2}\right)^{2}$$

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

$$m^{4}\times \left(2m^{\frac{5}{4}}\right)^{4}$$

Expand \left(2m^{\frac{5}{4}}\right)^{4}.

$$m^{4}\times 2^{4}\left(m^{\frac{5}{4}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply \frac{5}{4} and 4 to get 5.

$$m^{4}\times 2^{4}m^{5}$$

Calculate 2 to the power of 4 and get 16.

$$m^{4}\times 16m^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$m^{9}\times 16$$

Expand

$$16m^{9}$$

Solution Steps

Cancel out \sqrt{m} in both numerator and denominator.

$$\left(m^{2}\times \left(2m^{\frac{5}{4}}\right)^{2}\right)^{2}$$

Expand \left(m^{2}\times \left(2m^{\frac{5}{4}}\right)^{2}\right)^{2}.

$$\left(m^{2}\right)^{2}\times \left(\left(2m^{\frac{5}{4}}\right)^{2}\right)^{2}$$

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

$$m^{4}\times \left(\left(2m^{\frac{5}{4}}\right)^{2}\right)^{2}$$

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

$$m^{4}\times \left(2m^{\frac{5}{4}}\right)^{4}$$

Expand \left(2m^{\frac{5}{4}}\right)^{4}.

$$m^{4}\times 2^{4}\left(m^{\frac{5}{4}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply \frac{5}{4} and 4 to get 5.

$$m^{4}\times 2^{4}m^{5}$$

Calculate 2 to the power of 4 and get 16.

$$m^{4}\times 16m^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$m^{9}\times 16$$