Algebra Examples

${(x^{6} y^{4})}^{\frac{1}{8}} + 2 {(x^{\frac{1}{3}} y^{\frac{1}{4}})}^{2}$

Step 1

Apply the product rule to $x^{6} y^{4}$ .

${(x^{6})}^{\frac{1}{8}} {(y^{4})}^{\frac{1}{8}} + 2 {(x^{\frac{1}{3}} y^{\frac{1}{4}})}^{2}$

Step 2

Multiply the exponents in ${(x^{6})}^{\frac{1}{8}}$ .

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Step 2.1

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

$x^{6 (\frac{1}{8})} {(y^{4})}^{\frac{1}{8}} + 2 {(x^{\frac{1}{3}} y^{\frac{1}{4}})}^{2}$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $6$ .

$x^{2 (3) \frac{1}{8}} {(y^{4})}^{\frac{1}{8}} + 2 {(x^{\frac{1}{3}} y^{\frac{1}{4}})}^{2}$

Step 2.2.2

Factor $2$ out of $8$ .

$x^{2 \cdot 3 \frac{1}{2 \cdot 4}} {(y^{4})}^{\frac{1}{8}} + 2 {(x^{\frac{1}{3}} y^{\frac{1}{4}})}^{2}$

Step 2.2.3

Cancel the common factor.

$x^{2 \cdot 3 \frac{1}{2 \cdot 4}} {(y^{4})}^{\frac{1}{8}} + 2 {(x^{\frac{1}{3}} y^{\frac{1}{4}})}^{2}$

Step 2.2.4

Rewrite the expression.

$x^{3 (\frac{1}{4})} {(y^{4})}^{\frac{1}{8}} + 2 {(x^{\frac{1}{3}} y^{\frac{1}{4}})}^{2}$

Step 2.3

Combine $3$ and $\frac{1}{4}$ .

$x^{\frac{3}{4}} {(y^{4})}^{\frac{1}{8}} + 2 {(x^{\frac{1}{3}} y^{\frac{1}{4}})}^{2}$

Step 3

Multiply the exponents in ${(y^{4})}^{\frac{1}{8}}$ .

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Step 3.1

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

$x^{\frac{3}{4}} y^{4 (\frac{1}{8})} + 2 {(x^{\frac{1}{3}} y^{\frac{1}{4}})}^{2}$

Step 3.2

Cancel the common factor of $4$ .

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Step 3.2.1

Factor $4$ out of $8$ .

$x^{\frac{3}{4}} y^{4 \frac{1}{4 (2)}} + 2 {(x^{\frac{1}{3}} y^{\frac{1}{4}})}^{2}$

Step 3.2.2

Cancel the common factor.

$x^{\frac{3}{4}} y^{4 \frac{1}{4 \cdot 2}} + 2 {(x^{\frac{1}{3}} y^{\frac{1}{4}})}^{2}$

Step 3.2.3

Rewrite the expression.

$x^{\frac{3}{4}} y^{\frac{1}{2}} + 2 {(x^{\frac{1}{3}} y^{\frac{1}{4}})}^{2}$

Step 4

Apply the product rule to $x^{\frac{1}{3}} y^{\frac{1}{4}}$ .

$x^{\frac{3}{4}} y^{\frac{1}{2}} + 2 ({(x^{\frac{1}{3}})}^{2} {(y^{\frac{1}{4}})}^{2})$

Step 5

Multiply the exponents in ${(x^{\frac{1}{3}})}^{2}$ .

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Step 5.1

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

$x^{\frac{3}{4}} y^{\frac{1}{2}} + 2 (x^{\frac{1}{3} \cdot 2} {(y^{\frac{1}{4}})}^{2})$

Step 5.2

Combine $\frac{1}{3}$ and $2$ .

$x^{\frac{3}{4}} y^{\frac{1}{2}} + 2 (x^{\frac{2}{3}} {(y^{\frac{1}{4}})}^{2})$

Step 6

Multiply the exponents in ${(y^{\frac{1}{4}})}^{2}$ .

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Step 6.1

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

$x^{\frac{3}{4}} y^{\frac{1}{2}} + 2 (x^{\frac{2}{3}} y^{\frac{1}{4} \cdot 2})$

Step 6.2

Cancel the common factor of $2$ .

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Step 6.2.1

Factor $2$ out of $4$ .

$x^{\frac{3}{4}} y^{\frac{1}{2}} + 2 (x^{\frac{2}{3}} y^{\frac{1}{2 (2)} \cdot 2})$

Step 6.2.2

Cancel the common factor.

$x^{\frac{3}{4}} y^{\frac{1}{2}} + 2 (x^{\frac{2}{3}} y^{\frac{1}{2 \cdot 2} \cdot 2})$

Step 6.2.3

Rewrite the expression.

$x^{\frac{3}{4}} y^{\frac{1}{2}} + 2 (x^{\frac{2}{3}} y^{\frac{1}{2}})$

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