Algebra Examples

$3 {(x^{\frac{1}{2}} y^{3})}^{2} - {(x^{3} y^{18})}^{\frac{1}{3}}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $x^{\frac{1}{2}} y^{3}$ .

$3 ({(x^{\frac{1}{2}})}^{2} {(y^{3})}^{2}) - {(x^{3} y^{18})}^{\frac{1}{3}}$

Step 1.2

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

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Step 1.2.1

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

$3 (x^{\frac{1}{2} \cdot 2} {(y^{3})}^{2}) - {(x^{3} y^{18})}^{\frac{1}{3}}$

Step 1.2.2

Cancel the common factor of $2$ .

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Step 1.2.2.1

Cancel the common factor.

$3 (x^{\frac{1}{2} \cdot 2} {(y^{3})}^{2}) - {(x^{3} y^{18})}^{\frac{1}{3}}$

Step 1.2.2.2

Rewrite the expression.

$3 (x^{1} {(y^{3})}^{2}) - {(x^{3} y^{18})}^{\frac{1}{3}}$

Step 1.3

Simplify.

$3 (x {(y^{3})}^{2}) - {(x^{3} y^{18})}^{\frac{1}{3}}$

Step 1.4

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

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Step 1.4.1

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

$3 (x y^{3 \cdot 2}) - {(x^{3} y^{18})}^{\frac{1}{3}}$

Step 1.4.2

Multiply $3$ by $2$ .

$3 (x y^{6}) - {(x^{3} y^{18})}^{\frac{1}{3}}$

Step 1.5

Apply the product rule to $x^{3} y^{18}$ .

$3 x y^{6} - ({(x^{3})}^{\frac{1}{3}} {(y^{18})}^{\frac{1}{3}})$

Step 1.6

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

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Step 1.6.1

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

$3 x y^{6} - (x^{3 (\frac{1}{3})} {(y^{18})}^{\frac{1}{3}})$

Step 1.6.2

Cancel the common factor of $3$ .

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Step 1.6.2.1

Cancel the common factor.

$3 x y^{6} - (x^{3 (\frac{1}{3})} {(y^{18})}^{\frac{1}{3}})$

Step 1.6.2.2

Rewrite the expression.

$3 x y^{6} - (x^{1} {(y^{18})}^{\frac{1}{3}})$

Step 1.7

Simplify.

$3 x y^{6} - (x {(y^{18})}^{\frac{1}{3}})$

Step 1.8

Multiply the exponents in ${(y^{18})}^{\frac{1}{3}}$ .

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Step 1.8.1

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

$3 x y^{6} - (x y^{18 (\frac{1}{3})})$

Step 1.8.2

Cancel the common factor of $3$ .

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Step 1.8.2.1

Factor $3$ out of $18$ .

$3 x y^{6} - (x y^{3 (6) \frac{1}{3}})$

Step 1.8.2.2

Cancel the common factor.

$3 x y^{6} - (x y^{3 \cdot 6 \frac{1}{3}})$

Step 1.8.2.3

Rewrite the expression.

$3 x y^{6} - (x y^{6})$

$3 x y^{6} - x y^{6}$

Step 2

Subtract $x y^{6}$ from $3 x y^{6}$ .

$2 x y^{6}$