## anonymous 5 years ago my question.......

1. anonymous

$\sqrt[4]{486x ^{12}y ^{14}}$ simplify

2. anonymous

would it be $3x ^{3}y ^{3}$ on the oustide and then $\sqrt[4]{6y ^{2}}$

3. anonymous

4. anonymous

anyone could help my assignment please

5. anonymous

The first thing you should do is try to break 486 down into prime factors and put some into powers of 4. So, $486=2 \times 3^5$factored into primes. Now, we can write,$486=2 \times 3 \times 3^4=6\times 3^4$Now we can write,$(6 \times 3^4x^{12}y^{14})^{1/4}=6^{1/4}\times (3^4)^{1/4}\times (x^{12})^{1/4}\times (y^{14})^{1/4}$$=\sqrt[4]{6} \times 3^{4/4} \times x^{12/4} \times y ^{14/4}$$=\sqrt[4]{6}\times3\times x^3 \times y^{7/2}$$=3\sqrt[4]{6}x^3y^{7/2}$