Simplify (9^5 square root of 160x^8y^11)/(3^5 square root of 5xy^2)

$\frac{9^{5} \sqrt{160 x^{8} y^{11}}}{3^{5} \sqrt{5 x y^{2}}}$

Step 1

Combine $\sqrt{160 x^{8} y^{11}}$ and $\sqrt{5 x y^{2}}$ into a single radical.

$\frac{9^{5} \sqrt{\frac{160 x^{8} y^{11}}{5 x y^{2}}}}{3^{5}}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $160$ and $5$ .

Factor $5$ out of $160 x^{8} y^{11}$ .

$\frac{9^{5} \sqrt{\frac{5 (32 x^{8} y^{11})}{5 x y^{2}}}}{3^{5}}$

Cancel the common factors.

Factor $5$ out of $5 x y^{2}$ .

$\frac{9^{5} \sqrt{\frac{5 (32 x^{8} y^{11})}{5 (x y^{2})}}}{3^{5}}$

Cancel the common factor.

$\frac{9^{5} \sqrt{\frac{5 (32 x^{8} y^{11})}{5 (x y^{2})}}}{3^{5}}$

Rewrite the expression.

$\frac{9^{5} \sqrt{\frac{32 x^{8} y^{11}}{x y^{2}}}}{3^{5}}$

Cancel the common factor of $x^{8}$ and $x$ .

Factor $x$ out of $32 x^{8} y^{11}$ .

$\frac{9^{5} \sqrt{\frac{x (32 x^{7} y^{11})}{x y^{2}}}}{3^{5}}$

Cancel the common factors.

Factor $x$ out of $x y^{2}$ .

$\frac{9^{5} \sqrt{\frac{x (32 x^{7} y^{11})}{x (y^{2})}}}{3^{5}}$

Cancel the common factor.

$\frac{9^{5} \sqrt{\frac{x (32 x^{7} y^{11})}{x y^{2}}}}{3^{5}}$

Rewrite the expression.

$\frac{9^{5} \sqrt{\frac{32 x^{7} y^{11}}{y^{2}}}}{3^{5}}$

Cancel the common factor of $y^{11}$ and $y^{2}$ .

Factor $y^{2}$ out of $32 x^{7} y^{11}$ .

$\frac{9^{5} \sqrt{\frac{y^{2} (32 x^{7} y^{9})}{y^{2}}}}{3^{5}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{9^{5} \sqrt{\frac{y^{2} (32 x^{7} y^{9})}{y^{2} \cdot 1}}}{3^{5}}$

Cancel the common factor.

$\frac{9^{5} \sqrt{\frac{y^{2} (32 x^{7} y^{9})}{y^{2} \cdot 1}}}{3^{5}}$

Rewrite the expression.

$\frac{9^{5} \sqrt{\frac{32 x^{7} y^{9}}{1}}}{3^{5}}$

Divide $32 x^{7} y^{9}$ by $1$ .

$\frac{9^{5} \sqrt{32 x^{7} y^{9}}}{3^{5}}$

Step 3

Simplify the numerator.

Raise $9$ to the power of $5$ .

$\frac{59049 \sqrt{32 x^{7} y^{9}}}{3^{5}}$

Rewrite $32 x^{7} y^{9}$ as ${(4 x^{3} y^{4})}^{2} \cdot (2 x y)$ .

Factor $16$ out of $32$ .

$\frac{59049 \sqrt{16 (2) x^{7} y^{9}}}{3^{5}}$

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

$\frac{59049 \sqrt{4^{2} \cdot 2 x^{7} y^{9}}}{3^{5}}$

Factor out $x^{6}$ .

$\frac{59049 \sqrt{4^{2} \cdot 2 (x^{6} x) y^{9}}}{3^{5}}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$\frac{59049 \sqrt{4^{2} \cdot 2 ({(x^{3})}^{2} x) y^{9}}}{3^{5}}$

Factor out $y^{8}$ .

$\frac{59049 \sqrt{4^{2} \cdot 2 ({(x^{3})}^{2} x) (y^{8} y)}}{3^{5}}$

Rewrite $y^{8}$ as ${(y^{4})}^{2}$ .

$\frac{59049 \sqrt{4^{2} \cdot 2 ({(x^{3})}^{2} x) ({(y^{4})}^{2} y)}}{3^{5}}$

Move $x$ .

$\frac{59049 \sqrt{4^{2} \cdot 2 ({(x^{3})}^{2}) {(y^{4})}^{2} x y}}{3^{5}}$

Move $2$ .

$\frac{59049 \sqrt{4^{2} ({(x^{3})}^{2}) {(y^{4})}^{2} \cdot 2 x y}}{3^{5}}$

Rewrite $(4^{2} ({(x^{3})}^{2})) {(y^{4})}^{2}$ as ${(4 x^{3} y^{4})}^{2}$ .

$\frac{59049 \sqrt{{(4 x^{3} y^{4})}^{2} \cdot 2 x y}}{3^{5}}$

Add parentheses.

$\frac{59049 \sqrt{{(4 x^{3} y^{4})}^{2} \cdot 2 (x y)}}{3^{5}}$

Add parentheses.

$\frac{59049 \sqrt{{(4 x^{3} y^{4})}^{2} \cdot (2 x y)}}{3^{5}}$

Pull terms out from under the radical.

$\frac{59049 \cdot 4 x^{3} y^{4} \sqrt{2 x y}}{3^{5}}$

Multiply $59049$ by $4$ .

$\frac{236196 x^{3} y^{4} \sqrt{2 x y}}{3^{5}}$

Step 4

Reduce the expression by cancelling the common factors.

Raise $3$ to the power of $5$ .

$\frac{236196 x^{3} y^{4} \sqrt{2 x y}}{243}$

Cancel the common factor of $236196$ and $243$ .

Factor $243$ out of $236196 x^{3} y^{4} \sqrt{2 x y}$ .

$\frac{243 (972 x^{3} y^{4} \sqrt{2 x y})}{243}$

Cancel the common factors.

Factor $243$ out of $243$ .

$\frac{243 (972 x^{3} y^{4} \sqrt{2 x y})}{243 (1)}$

Cancel the common factor.

$\frac{243 (972 x^{3} y^{4} \sqrt{2 x y})}{243 \cdot 1}$

Rewrite the expression.

$\frac{972 x^{3} y^{4} \sqrt{2 x y}}{1}$

Divide $972 x^{3} y^{4} \sqrt{2 x y}$ by $1$ .

$972 x^{3} y^{4} \sqrt{2 x y}$

Simplify (9^5 square root of 160x^8y^11)/(3^5 square root of 5xy^2)

Related Questions

Support LCMGCF.com by disabling your adblocker.