Algebra Examples

$\sqrt[4]{\frac{81}{16} a^{8} b^{12} c^{16}}$

Step 1

Combine $\frac{81}{16}$ and $a^{8}$ .

$\sqrt[4]{\frac{81 a^{8}}{16} b^{12} c^{16}}$

Step 2

Combine $\frac{81 a^{8}}{16}$ and $b^{12}$ .

$\sqrt[4]{\frac{81 a^{8} b^{12}}{16} c^{16}}$

Step 3

Combine $\frac{81 a^{8} b^{12}}{16}$ and $c^{16}$ .

$\sqrt[4]{\frac{81 a^{8} b^{12} c^{16}}{16}}$

Step 4

Rewrite $81 a^{8} b^{12} c^{16}$ as ${(3 a^{2} b^{3} c^{4})}^{4}$ .

$\sqrt[4]{\frac{{(3 a^{2} b^{3} c^{4})}^{4}}{16}}$

Step 5

Rewrite $16$ as $2^{4}$ .

$\sqrt[4]{\frac{{(3 a^{2} b^{3} c^{4})}^{4}}{2^{4}}}$

Step 6

Rewrite $\frac{{(3 a^{2} b^{3} c^{4})}^{4}}{2^{4}}$ as ${(\frac{3 a^{2} b^{3} c^{4}}{2})}^{4}$ .

$\sqrt[4]{{(\frac{3 a^{2} b^{3} c^{4}}{2})}^{4}}$

Step 7

Pull terms out from under the radical, assuming positive real numbers.

$\frac{3 a^{2} b^{3} c^{4}}{2}$