Evaluate (-2/3)/(( square root of 5)/3)

$\frac{- \frac{2}{3}}{\frac{\sqrt{5}}{3}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$- \frac{2}{3} \cdot \frac{3}{\sqrt{5}}$

Step 2

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{3}{\sqrt{5}}$

Cancel the common factor.

$\frac{- 2}{3} \cdot \frac{3}{\sqrt{5}}$

Rewrite the expression.

$- 2 \frac{1}{\sqrt{5}}$

Step 3

Combine $- 2$ and $\frac{1}{\sqrt{5}}$ .

$\frac{- 2}{\sqrt{5}}$

Step 4

Move the negative in front of the fraction.

$- \frac{2}{\sqrt{5}}$

Step 5

Multiply $\frac{2}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$- (\frac{2}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}})$

Step 6

Combine and simplify the denominator.

Multiply $\frac{2}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$- \frac{2 \sqrt{5}}{\sqrt{5} \sqrt{5}}$

Raise $\sqrt{5}$ to the power of $1$ .

$- \frac{2 \sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}}$

Raise $\sqrt{5}$ to the power of $1$ .

$- \frac{2 \sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}}$

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

$- \frac{2 \sqrt{5}}{{\sqrt{5}}^{1 + 1}}$

Add $1$ and $1$ .

$- \frac{2 \sqrt{5}}{{\sqrt{5}}^{2}}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$- \frac{2 \sqrt{5}}{{(5^{\frac{1}{2}})}^{2}}$

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

$- \frac{2 \sqrt{5}}{5^{\frac{1}{2} \cdot 2}}$

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

$- \frac{2 \sqrt{5}}{5^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{2 \sqrt{5}}{5^{\frac{2}{2}}}$

Rewrite the expression.

$- \frac{2 \sqrt{5}}{5^{1}}$

Evaluate the exponent.

$- \frac{2 \sqrt{5}}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{2 \sqrt{5}}{5}$

Decimal Form:

$- 0.89442719 \dots$

Evaluate (-2/3)/(( square root of 5)/3)

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