Algebra Examples

${(\frac{16 x^{13}}{y^{15}})}^{\frac{1}{3}}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 1.1

Apply the product rule to $\frac{16 x^{13}}{y^{15}}$ .

$\frac{{(16 x^{13})}^{\frac{1}{3}}}{{(y^{15})}^{\frac{1}{3}}}$

Step 1.2

Apply the product rule to $16 x^{13}$ .

$\frac{16^{\frac{1}{3}} {(x^{13})}^{\frac{1}{3}}}{{(y^{15})}^{\frac{1}{3}}}$

Step 2

Multiply the exponents in ${(x^{13})}^{\frac{1}{3}}$ .

Tap for more steps...

Step 2.1

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

$\frac{16^{\frac{1}{3}} x^{13 (\frac{1}{3})}}{{(y^{15})}^{\frac{1}{3}}}$

Step 2.2

Combine $13$ and $\frac{1}{3}$ .

$\frac{16^{\frac{1}{3}} x^{\frac{13}{3}}}{{(y^{15})}^{\frac{1}{3}}}$

Step 3

Multiply the exponents in ${(y^{15})}^{\frac{1}{3}}$ .

Tap for more steps...

Step 3.1

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

$\frac{16^{\frac{1}{3}} x^{\frac{13}{3}}}{y^{15 (\frac{1}{3})}}$

Step 3.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.1

Factor $3$ out of $15$ .

$\frac{16^{\frac{1}{3}} x^{\frac{13}{3}}}{y^{3 (5) \frac{1}{3}}}$

Step 3.2.2

Cancel the common factor.

$\frac{16^{\frac{1}{3}} x^{\frac{13}{3}}}{y^{3 \cdot 5 \frac{1}{3}}}$

Step 3.2.3

Rewrite the expression.

$\frac{16^{\frac{1}{3}} x^{\frac{13}{3}}}{y^{5}}$