Solve {left(3{w}^frac{3{4}}right)}^2{left(5{w}^frac{1{2}}right)}^2

$${ \left(3 { w }^{ \frac{ 3 }{ 4 } } \right) }^{ 2 } { \left(5 { w }^{ \frac{ 1 }{ 2 } } \right) }^{ 2 }$$

Evaluate

$$225w^{\frac{5}{2}}$$

Solution Steps

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

$$3^{2}\left(w^{\frac{3}{4}}\right)^{2}\times \left(5w^{\frac{1}{2}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{3}{4} and 2 to get \frac{3}{2}.

$$3^{2}w^{\frac{3}{2}}\times \left(5w^{\frac{1}{2}}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9w^{\frac{3}{2}}\times \left(5w^{\frac{1}{2}}\right)^{2}$$

Expand \left(5w^{\frac{1}{2}}\right)^{2}.

$$9w^{\frac{3}{2}}\times 5^{2}\left(w^{\frac{1}{2}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and 2 to get 1.

$$9w^{\frac{3}{2}}\times 5^{2}w^{1}$$

Calculate 5 to the power of 2 and get 25.

$$9w^{\frac{3}{2}}\times 25w^{1}$$

Calculate w to the power of 1 and get w.

$$9w^{\frac{3}{2}}\times 25w$$

Multiply 9 and 25 to get 225.

$$225w^{\frac{3}{2}}w$$

To multiply powers of the same base, add their exponents. Add \frac{3}{2} and 1 to get \frac{5}{2}.

$$225w^{\frac{5}{2}}$$

Expand

$$225w^{\frac{5}{2}}$$

Solution Steps

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

$$3^{2}\left(w^{\frac{3}{4}}\right)^{2}\times \left(5w^{\frac{1}{2}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{3}{4} and 2 to get \frac{3}{2}.

$$3^{2}w^{\frac{3}{2}}\times \left(5w^{\frac{1}{2}}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9w^{\frac{3}{2}}\times \left(5w^{\frac{1}{2}}\right)^{2}$$

Expand \left(5w^{\frac{1}{2}}\right)^{2}.

$$9w^{\frac{3}{2}}\times 5^{2}\left(w^{\frac{1}{2}}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and 2 to get 1.

$$9w^{\frac{3}{2}}\times 5^{2}w^{1}$$

Calculate 5 to the power of 2 and get 25.

$$9w^{\frac{3}{2}}\times 25w^{1}$$

Calculate w to the power of 1 and get w.

$$9w^{\frac{3}{2}}\times 25w$$

Multiply 9 and 25 to get 225.

$$225w^{\frac{3}{2}}w$$

To multiply powers of the same base, add their exponents. Add \frac{3}{2} and 1 to get \frac{5}{2}.

$$225w^{\frac{5}{2}}$$