Solve (3a^frac{1{2}}b^frac{1{2}})^2

$$( 3 a ^ { \frac { 1 } { 2 } } b ^ { \frac { 1 } { 2 } } ) ^ { 2 }$$

Evaluate

$$9ab$$

Solution Steps

Expand \left(3a^{\frac{1}{2}}b^{\frac{1}{2}}\right)^{2}.

$$3^{2}\left(a^{\frac{1}{2}}\right)^{2}\left(b^{\frac{1}{2}}\right)^{2}$$

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

$$3^{2}a^{1}\left(b^{\frac{1}{2}}\right)^{2}$$

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

$$3^{2}a^{1}b^{1}$$

Calculate 3 to the power of 2 and get 9.

$$9a^{1}b^{1}$$

Calculate a to the power of 1 and get a.

$$9ab^{1}$$

Calculate b to the power of 1 and get b.

$$9ab$$

Expand

$$9ab$$

Solution Steps

Expand \left(3a^{\frac{1}{2}}b^{\frac{1}{2}}\right)^{2}.

$$3^{2}\left(a^{\frac{1}{2}}\right)^{2}\left(b^{\frac{1}{2}}\right)^{2}$$

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

$$3^{2}a^{1}\left(b^{\frac{1}{2}}\right)^{2}$$

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

$$3^{2}a^{1}b^{1}$$

Calculate 3 to the power of 2 and get 9.

$$9a^{1}b^{1}$$

Calculate a to the power of 1 and get a.

$$9ab^{1}$$

Calculate b to the power of 1 and get b.

$$9ab$$