Solve 3^frac{1{2}}*3^frac{3{2}}=3^frac{1{2}+3/2}

$$3 ^ { \frac { 1 } { 2 } } \times 3 ^ { \frac { 3 } { 2 } } = 3 ^ { \frac { 1 } { 2 } + \frac { 3 } { 2 } }$$

Verify

Solution Steps

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

$$3^{2}=3^{\frac{1}{2}+\frac{3}{2}}$$

Calculate 3 to the power of 2 and get 9.

$$9=3^{\frac{1}{2}+\frac{3}{2}}$$

Add \frac{1}{2} and \frac{3}{2} to get 2.

$$9=3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9=9$$

Compare 9 and 9.

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