Finite Math Examples

$\sqrt[3]{625 x y^{3}} + y \sqrt[3]{40 x}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{625 x y^{3}}$ as ${(625 x y^{3})}^{\frac{1}{3}}$ .

${(625 x y^{3})}^{\frac{1}{3}} + y \sqrt[3]{40 x}$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{40 x}$ as ${(40 x)}^{\frac{1}{3}}$ .

${(625 x y^{3})}^{\frac{1}{3}} + y {(40 x)}^{\frac{1}{3}}$

Step 3

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

Tap for more steps...

Step 3.1

Apply the product rule to $625 x y^{3}$ .

${(625 x)}^{\frac{1}{3}} {(y^{3})}^{\frac{1}{3}} + y {(40 x)}^{\frac{1}{3}}$

Step 3.2

Apply the product rule to $625 x$ .

$625^{\frac{1}{3}} x^{\frac{1}{3}} {(y^{3})}^{\frac{1}{3}} + y {(40 x)}^{\frac{1}{3}}$

Step 4

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

Tap for more steps...

Step 4.1

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

$625^{\frac{1}{3}} x^{\frac{1}{3}} y^{3 (\frac{1}{3})} + y {(40 x)}^{\frac{1}{3}}$

Step 4.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.1

Cancel the common factor.

$625^{\frac{1}{3}} x^{\frac{1}{3}} y^{3 (\frac{1}{3})} + y {(40 x)}^{\frac{1}{3}}$

Step 4.2.2

Rewrite the expression.

$625^{\frac{1}{3}} x^{\frac{1}{3}} y^{1} + y {(40 x)}^{\frac{1}{3}}$

Step 5

Simplify.

$625^{\frac{1}{3}} x^{\frac{1}{3}} y + y {(40 x)}^{\frac{1}{3}}$

Step 6

Apply the product rule to $40 x$ .

$625^{\frac{1}{3}} x^{\frac{1}{3}} y + y (40^{\frac{1}{3}} x^{\frac{1}{3}})$

Step 7

Rewrite using the commutative property of multiplication.

$625^{\frac{1}{3}} x^{\frac{1}{3}} y + 40^{\frac{1}{3}} y x^{\frac{1}{3}}$

Step 8

Factor $x^{\frac{1}{3}} y$ out of $625^{\frac{1}{3}} x^{\frac{1}{3}} y + 40^{\frac{1}{3}} y x^{\frac{1}{3}}$ .

Tap for more steps...

Step 8.1

Move $y$ .

$625^{\frac{1}{3}} x^{\frac{1}{3}} y + 40^{\frac{1}{3}} x^{\frac{1}{3}} y$

Step 8.2

Factor $x^{\frac{1}{3}} y$ out of $625^{\frac{1}{3}} x^{\frac{1}{3}} y$ .

$x^{\frac{1}{3}} y (625^{\frac{1}{3}}) + 40^{\frac{1}{3}} x^{\frac{1}{3}} y$

Step 8.3

Factor $x^{\frac{1}{3}} y$ out of $40^{\frac{1}{3}} x^{\frac{1}{3}} y$ .

$x^{\frac{1}{3}} y (625^{\frac{1}{3}}) + x^{\frac{1}{3}} y (40^{\frac{1}{3}})$

Step 8.4

Factor $x^{\frac{1}{3}} y$ out of $x^{\frac{1}{3}} y (625^{\frac{1}{3}}) + x^{\frac{1}{3}} y (40^{\frac{1}{3}})$ .

$x^{\frac{1}{3}} y (625^{\frac{1}{3}} + 40^{\frac{1}{3}})$