Evaluate (3 square root of 3)(5 square root of 3)

$(3 \sqrt{3}) (5 \sqrt{3})$

Multiply $(3 \sqrt{3}) (5 \sqrt{3})$ .

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Multiply $5$ by $3$ .

$15 \sqrt{3} \sqrt{3}$

Raise $\sqrt{3}$ to the power of $1$ .

$15 ({\sqrt{3}}^{1} \sqrt{3})$

Raise $\sqrt{3}$ to the power of $1$ .

$15 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$15 {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

$15 {\sqrt{3}}^{2}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$15 {(3^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$15 \cdot 3^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$15 \cdot 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$15 \cdot 3^{\frac{2}{2}}$

Divide $1$ by $1$ .

$15 \cdot 3^{1}$

Evaluate the exponent.

$15 \cdot 3$

Multiply $15$ by $3$ .

$45$

Evaluate (3 square root of 3)(5 square root of 3)

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