Basic Math Examples

$\frac{3^{\frac{2}{5}} y^{- \frac{1}{4}} z^{\frac{2}{5}}}{3^{- \frac{8}{5}} y^{\frac{7}{4}}}$

Step 1

Move $y^{- \frac{1}{4}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{3^{\frac{2}{5}} z^{\frac{2}{5}}}{3^{- \frac{8}{5}} y^{\frac{7}{4}} y^{\frac{1}{4}}}$

Step 2

Multiply $y^{\frac{7}{4}}$ by $y^{\frac{1}{4}}$ by adding the exponents.

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Step 2.1

Move $y^{\frac{1}{4}}$ .

$\frac{3^{\frac{2}{5}} z^{\frac{2}{5}}}{3^{- \frac{8}{5}} (y^{\frac{1}{4}} y^{\frac{7}{4}})}$

Step 2.2

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

$\frac{3^{\frac{2}{5}} z^{\frac{2}{5}}}{3^{- \frac{8}{5}} y^{\frac{1}{4} + \frac{7}{4}}}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{3^{\frac{2}{5}} z^{\frac{2}{5}}}{3^{- \frac{8}{5}} y^{\frac{1 + 7}{4}}}$

Step 2.4

Add $1$ and $7$ .

$\frac{3^{\frac{2}{5}} z^{\frac{2}{5}}}{3^{- \frac{8}{5}} y^{\frac{8}{4}}}$

Step 2.5

Divide $8$ by $4$ .

$\frac{3^{\frac{2}{5}} z^{\frac{2}{5}}}{3^{- \frac{8}{5}} y^{2}}$

Step 3

Move $3^{- \frac{8}{5}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{3^{\frac{2}{5}} z^{\frac{2}{5}} \cdot 3^{\frac{8}{5}}}{y^{2}}$

Step 4

Multiply $3^{\frac{2}{5}}$ by $3^{\frac{8}{5}}$ by adding the exponents.

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Step 4.1

Move $3^{\frac{8}{5}}$ .

$\frac{3^{\frac{8}{5}} \cdot 3^{\frac{2}{5}} z^{\frac{2}{5}}}{y^{2}}$

Step 4.2

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

$\frac{3^{\frac{8}{5} + \frac{2}{5}} z^{\frac{2}{5}}}{y^{2}}$

Step 4.3

Combine the numerators over the common denominator.

$\frac{3^{\frac{8 + 2}{5}} z^{\frac{2}{5}}}{y^{2}}$

Step 4.4

Add $8$ and $2$ .

$\frac{3^{\frac{10}{5}} z^{\frac{2}{5}}}{y^{2}}$

Step 4.5

Divide $10$ by $5$ .

$\frac{3^{2} z^{\frac{2}{5}}}{y^{2}}$

Step 5

Raise $3$ to the power of $2$ .

$\frac{9 z^{\frac{2}{5}}}{y^{2}}$