Basic Math Examples

$8 \sqrt{y} \cdot (- 2 \sqrt{y})$

Step 1

Multiply $8 \sqrt{y} (- 2 \sqrt{y})$ .

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Step 1.1

Multiply $- 2$ by $8$ .

$- 16 \sqrt{y} \sqrt{y}$

Step 1.2

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

$- 16 ({\sqrt{y}}^{1} \sqrt{y})$

Step 1.3

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

$- 16 ({\sqrt{y}}^{1} {\sqrt{y}}^{1})$

Step 1.4

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

$- 16 {\sqrt{y}}^{1 + 1}$

Step 1.5

Add $1$ and $1$ .

$- 16 {\sqrt{y}}^{2}$

Step 2

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

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Step 2.1

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

$- 16 {(y^{\frac{1}{2}})}^{2}$

Step 2.2

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

$- 16 y^{\frac{1}{2} \cdot 2}$

Step 2.3

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

$- 16 y^{\frac{2}{2}}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$- 16 y^{\frac{2}{2}}$

Step 2.4.2

Rewrite the expression.

$- 16 y^{1}$

Step 2.5

Simplify.

$- 16 y$