Simplify ((x^2)/z)^3((6z^3y)/(2y^2))+ square root of (4^0)/(z^4)

${(\frac{x^{2}}{z})}^{3} (\frac{6 z^{3} y}{2 y^{2}}) + \sqrt{\frac{4^{0}}{z^{4}}}$

Step 1

Apply the product rule to $\frac{x^{2}}{z}$ .

$\frac{{(x^{2})}^{3}}{z^{3}} \cdot \frac{6 z^{3} y}{2 y^{2}} + \sqrt{\frac{4^{0}}{z^{4}}}$

Step 2

Combine.

$\frac{{(x^{2})}^{3} (6 z^{3} y)}{z^{3} (2 y^{2})} + \sqrt{\frac{4^{0}}{z^{4}}}$

Step 3

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of ${(x^{2})}^{3} (6 z^{3} y)$ .

$\frac{2 ({(x^{2})}^{3} (3 z^{3} y))}{z^{3} (2 y^{2})} + \sqrt{\frac{4^{0}}{z^{4}}}$

Cancel the common factors.

Factor $2$ out of $z^{3} (2 y^{2})$ .

$\frac{2 ({(x^{2})}^{3} (3 z^{3} y))}{2 (z^{3} (y^{2}))} + \sqrt{\frac{4^{0}}{z^{4}}}$

Cancel the common factor.

$\frac{2 ({(x^{2})}^{3} (3 z^{3} y))}{2 (z^{3} (y^{2}))} + \sqrt{\frac{4^{0}}{z^{4}}}$

Rewrite the expression.

$\frac{{(x^{2})}^{3} (3 z^{3} y)}{z^{3} (y^{2})} + \sqrt{\frac{4^{0}}{z^{4}}}$

Step 4

Cancel the common factor of $z^{3}$ .

Cancel the common factor.

$\frac{{(x^{2})}^{3} (3 z^{3} y)}{z^{3} y^{2}} + \sqrt{\frac{4^{0}}{z^{4}}}$

Rewrite the expression.

$\frac{{(x^{2})}^{3} (3 y)}{y^{2}} + \sqrt{\frac{4^{0}}{z^{4}}}$

Step 5

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

Factor $y$ out of ${(x^{2})}^{3} (3 y)$ .

$\frac{y ({(x^{2})}^{3} \cdot (3))}{y^{2}} + \sqrt{\frac{4^{0}}{z^{4}}}$

Cancel the common factors.

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

$\frac{y ({(x^{2})}^{3} \cdot (3))}{y \cdot y} + \sqrt{\frac{4^{0}}{z^{4}}}$

Cancel the common factor.

$\frac{y ({(x^{2})}^{3} \cdot (3))}{y \cdot y} + \sqrt{\frac{4^{0}}{z^{4}}}$

Rewrite the expression.

$\frac{{(x^{2})}^{3} \cdot (3)}{y} + \sqrt{\frac{4^{0}}{z^{4}}}$

Step 6

Multiply the exponents in ${(x^{2})}^{3}$ .

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

$\frac{x^{2 \cdot 3} \cdot 3}{y} + \sqrt{\frac{4^{0}}{z^{4}}}$

Multiply $2$ by $3$ .

$\frac{x^{6} \cdot 3}{y} + \sqrt{\frac{4^{0}}{z^{4}}}$

Step 7

Move $3$ to the left of $x^{6}$ .

$\frac{3 \cdot x^{6}}{y} + \sqrt{\frac{4^{0}}{z^{4}}}$

Step 8

Anything raised to $0$ is $1$ .

$\frac{3 x^{6}}{y} + \sqrt{\frac{1}{z^{4}}}$

Step 9

Rewrite $1$ as $1^{2}$ .

$\frac{3 x^{6}}{y} + \sqrt{\frac{1^{2}}{z^{4}}}$

Step 10

Rewrite $z^{4}$ as ${(z^{2})}^{2}$ .

$\frac{3 x^{6}}{y} + \sqrt{\frac{1^{2}}{{(z^{2})}^{2}}}$

Step 11

Rewrite $\frac{1^{2}}{{(z^{2})}^{2}}$ as ${(\frac{1}{z^{2}})}^{2}$ .

$\frac{3 x^{6}}{y} + \sqrt{{(\frac{1}{z^{2}})}^{2}}$

Step 12

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

$\frac{3 x^{6}}{y} + \frac{1}{z^{2}}$

Simplify ((x^2)/z)^3((6z^3y)/(2y^2))+ square root of (4^0)/(z^4)

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