Basic Math Examples

$\frac{{(\sqrt[3]{y - 2})}^{2}}{{(\sqrt[5]{y - 2})}^{2}}$

Step 1

Rewrite ${\sqrt[3]{y - 2}}^{2}$ as $\sqrt[3]{{(y - 2)}^{2}}$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}}}{{\sqrt[5]{y - 2}}^{2}}$

Step 2

Rewrite ${\sqrt[5]{y - 2}}^{2}$ as $\sqrt[5]{{(y - 2)}^{2}}$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}}}{\sqrt[5]{{(y - 2)}^{2}}}$

Step 3

Multiply $\frac{\sqrt[3]{{(y - 2)}^{2}}}{\sqrt[5]{{(y - 2)}^{2}}}$ by $\frac{{\sqrt[5]{{(y - 2)}^{2}}}^{4}}{{\sqrt[5]{{(y - 2)}^{2}}}^{4}}$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}}}{\sqrt[5]{{(y - 2)}^{2}}} \cdot \frac{{\sqrt[5]{{(y - 2)}^{2}}}^{4}}{{\sqrt[5]{{(y - 2)}^{2}}}^{4}}$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{\sqrt[3]{{(y - 2)}^{2}}}{\sqrt[5]{{(y - 2)}^{2}}}$ by $\frac{{\sqrt[5]{{(y - 2)}^{2}}}^{4}}{{\sqrt[5]{{(y - 2)}^{2}}}^{4}}$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} {\sqrt[5]{{(y - 2)}^{2}}}^{4}}{\sqrt[5]{{(y - 2)}^{2}} {\sqrt[5]{{(y - 2)}^{2}}}^{4}}$

Step 4.2

Raise $\sqrt[5]{{(y - 2)}^{2}}$ to the power of $1$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} {\sqrt[5]{{(y - 2)}^{2}}}^{4}}{{\sqrt[5]{{(y - 2)}^{2}}}^{1} {\sqrt[5]{{(y - 2)}^{2}}}^{4}}$

Step 4.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt[3]{{(y - 2)}^{2}} {\sqrt[5]{{(y - 2)}^{2}}}^{4}}{{\sqrt[5]{{(y - 2)}^{2}}}^{1 + 4}}$

Step 4.4

Add $1$ and $4$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} {\sqrt[5]{{(y - 2)}^{2}}}^{4}}{{\sqrt[5]{{(y - 2)}^{2}}}^{5}}$

Step 4.5

Rewrite ${\sqrt[5]{{(y - 2)}^{2}}}^{5}$ as ${(y - 2)}^{2}$ .

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Step 4.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{{(y - 2)}^{2}}$ as ${(y - 2)}^{\frac{2}{5}}$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} {\sqrt[5]{{(y - 2)}^{2}}}^{4}}{{({(y - 2)}^{\frac{2}{5}})}^{5}}$

Step 4.5.2

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

$\frac{\sqrt[3]{{(y - 2)}^{2}} {\sqrt[5]{{(y - 2)}^{2}}}^{4}}{{(y - 2)}^{\frac{2}{5} \cdot 5}}$

Step 4.5.3

Combine $\frac{2}{5}$ and $5$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} {\sqrt[5]{{(y - 2)}^{2}}}^{4}}{{(y - 2)}^{\frac{2 \cdot 5}{5}}}$

Step 4.5.4

Multiply $2$ by $5$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} {\sqrt[5]{{(y - 2)}^{2}}}^{4}}{{(y - 2)}^{\frac{10}{5}}}$

Step 4.5.5

Cancel the common factor of $10$ and $5$ .

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Step 4.5.5.1

Factor $5$ out of $10$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} {\sqrt[5]{{(y - 2)}^{2}}}^{4}}{{(y - 2)}^{\frac{5 \cdot 2}{5}}}$

Step 4.5.5.2

Cancel the common factors.

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Step 4.5.5.2.1

Factor $5$ out of $5$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} {\sqrt[5]{{(y - 2)}^{2}}}^{4}}{{(y - 2)}^{\frac{5 \cdot 2}{5 (1)}}}$

Step 4.5.5.2.2

Cancel the common factor.

$\frac{\sqrt[3]{{(y - 2)}^{2}} {\sqrt[5]{{(y - 2)}^{2}}}^{4}}{{(y - 2)}^{\frac{5 \cdot 2}{5 \cdot 1}}}$

Step 4.5.5.2.3

Rewrite the expression.

$\frac{\sqrt[3]{{(y - 2)}^{2}} {\sqrt[5]{{(y - 2)}^{2}}}^{4}}{{(y - 2)}^{\frac{2}{1}}}$

Step 4.5.5.2.4

Divide $2$ by $1$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} {\sqrt[5]{{(y - 2)}^{2}}}^{4}}{{(y - 2)}^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite ${\sqrt[5]{{(y - 2)}^{2}}}^{4}$ as $\sqrt[5]{{({(y - 2)}^{2})}^{4}}$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{{({(y - 2)}^{2})}^{4}}}{{(y - 2)}^{2}}$

Step 5.2

Multiply the exponents in ${({(y - 2)}^{2})}^{4}$ .

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Step 5.2.1

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

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{{(y - 2)}^{2 \cdot 4}}}{{(y - 2)}^{2}}$

Step 5.2.2

Multiply $2$ by $4$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{{(y - 2)}^{8}}}{{(y - 2)}^{2}}$

Step 5.3

Use the Binomial Theorem.

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{y^{8} + 8 y^{7} \cdot - 2 + 28 y^{6} {(- 2)}^{2} + 56 y^{5} {(- 2)}^{3} + 70 y^{4} {(- 2)}^{4} + 56 y^{3} {(- 2)}^{5} + 28 y^{2} {(- 2)}^{6} + 8 y {(- 2)}^{7} + {(- 2)}^{8}}}{{(y - 2)}^{2}}$

Step 5.4

Simplify each term.

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Step 5.4.1

Multiply $- 2$ by $8$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{y^{8} - 16 y^{7} + 28 y^{6} {(- 2)}^{2} + 56 y^{5} {(- 2)}^{3} + 70 y^{4} {(- 2)}^{4} + 56 y^{3} {(- 2)}^{5} + 28 y^{2} {(- 2)}^{6} + 8 y {(- 2)}^{7} + {(- 2)}^{8}}}{{(y - 2)}^{2}}$

Step 5.4.2

Raise $- 2$ to the power of $2$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{y^{8} - 16 y^{7} + 28 y^{6} \cdot 4 + 56 y^{5} {(- 2)}^{3} + 70 y^{4} {(- 2)}^{4} + 56 y^{3} {(- 2)}^{5} + 28 y^{2} {(- 2)}^{6} + 8 y {(- 2)}^{7} + {(- 2)}^{8}}}{{(y - 2)}^{2}}$

Step 5.4.3

Multiply $4$ by $28$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{y^{8} - 16 y^{7} + 112 y^{6} + 56 y^{5} {(- 2)}^{3} + 70 y^{4} {(- 2)}^{4} + 56 y^{3} {(- 2)}^{5} + 28 y^{2} {(- 2)}^{6} + 8 y {(- 2)}^{7} + {(- 2)}^{8}}}{{(y - 2)}^{2}}$

Step 5.4.4

Raise $- 2$ to the power of $3$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{y^{8} - 16 y^{7} + 112 y^{6} + 56 y^{5} \cdot - 8 + 70 y^{4} {(- 2)}^{4} + 56 y^{3} {(- 2)}^{5} + 28 y^{2} {(- 2)}^{6} + 8 y {(- 2)}^{7} + {(- 2)}^{8}}}{{(y - 2)}^{2}}$

Step 5.4.5

Multiply $- 8$ by $56$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{y^{8} - 16 y^{7} + 112 y^{6} - 448 y^{5} + 70 y^{4} {(- 2)}^{4} + 56 y^{3} {(- 2)}^{5} + 28 y^{2} {(- 2)}^{6} + 8 y {(- 2)}^{7} + {(- 2)}^{8}}}{{(y - 2)}^{2}}$

Step 5.4.6

Raise $- 2$ to the power of $4$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{y^{8} - 16 y^{7} + 112 y^{6} - 448 y^{5} + 70 y^{4} \cdot 16 + 56 y^{3} {(- 2)}^{5} + 28 y^{2} {(- 2)}^{6} + 8 y {(- 2)}^{7} + {(- 2)}^{8}}}{{(y - 2)}^{2}}$

Step 5.4.7

Multiply $16$ by $70$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{y^{8} - 16 y^{7} + 112 y^{6} - 448 y^{5} + 1120 y^{4} + 56 y^{3} {(- 2)}^{5} + 28 y^{2} {(- 2)}^{6} + 8 y {(- 2)}^{7} + {(- 2)}^{8}}}{{(y - 2)}^{2}}$

Step 5.4.8

Raise $- 2$ to the power of $5$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{y^{8} - 16 y^{7} + 112 y^{6} - 448 y^{5} + 1120 y^{4} + 56 y^{3} \cdot - 32 + 28 y^{2} {(- 2)}^{6} + 8 y {(- 2)}^{7} + {(- 2)}^{8}}}{{(y - 2)}^{2}}$

Step 5.4.9

Multiply $- 32$ by $56$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{y^{8} - 16 y^{7} + 112 y^{6} - 448 y^{5} + 1120 y^{4} - 1792 y^{3} + 28 y^{2} {(- 2)}^{6} + 8 y {(- 2)}^{7} + {(- 2)}^{8}}}{{(y - 2)}^{2}}$

Step 5.4.10

Raise $- 2$ to the power of $6$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{y^{8} - 16 y^{7} + 112 y^{6} - 448 y^{5} + 1120 y^{4} - 1792 y^{3} + 28 y^{2} \cdot 64 + 8 y {(- 2)}^{7} + {(- 2)}^{8}}}{{(y - 2)}^{2}}$

Step 5.4.11

Multiply $64$ by $28$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{y^{8} - 16 y^{7} + 112 y^{6} - 448 y^{5} + 1120 y^{4} - 1792 y^{3} + 1792 y^{2} + 8 y {(- 2)}^{7} + {(- 2)}^{8}}}{{(y - 2)}^{2}}$

Step 5.4.12

Raise $- 2$ to the power of $7$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{y^{8} - 16 y^{7} + 112 y^{6} - 448 y^{5} + 1120 y^{4} - 1792 y^{3} + 1792 y^{2} + 8 y \cdot - 128 + {(- 2)}^{8}}}{{(y - 2)}^{2}}$

Step 5.4.13

Multiply $- 128$ by $8$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{y^{8} - 16 y^{7} + 112 y^{6} - 448 y^{5} + 1120 y^{4} - 1792 y^{3} + 1792 y^{2} - 1024 y + {(- 2)}^{8}}}{{(y - 2)}^{2}}$

Step 5.4.14

Raise $- 2$ to the power of $8$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{y^{8} - 16 y^{7} + 112 y^{6} - 448 y^{5} + 1120 y^{4} - 1792 y^{3} + 1792 y^{2} - 1024 y + 256}}{{(y - 2)}^{2}}$

Step 5.5

Make each term match the terms from the binomial theorem formula.

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{y^{8} - 8 \cdot 2 y^{7} + 28 \cdot 2^{2} y^{6} - 56 \cdot 2^{3} y^{5} + 70 \cdot 2^{4} y^{4} - 56 \cdot 2^{5} y^{3} + 28 \cdot 2^{6} y^{2} - 8 \cdot 2^{7} y + 2^{8}}}{{(y - 2)}^{2}}$

Step 5.6

Factor $y^{8} - 8 \cdot 2 y^{7} + 28 \cdot 2^{2} y^{6} - 56 \cdot 2^{3} y^{5} + 70 \cdot 2^{4} y^{4} - 56 \cdot 2^{5} y^{3} + 28 \cdot 2^{6} y^{2} - 8 \cdot 2^{7} y + 2^{8}$ using the binomial theorem.

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{{(2 - y)}^{8}}}{{(y - 2)}^{2}}$

Step 5.7

Factor out ${(2 - y)}^{5}$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{{(2 - y)}^{5} {(2 - y)}^{3}}}{{(y - 2)}^{2}}$

Step 5.8

Pull terms out from under the radical.

$\frac{\sqrt[3]{{(y - 2)}^{2}} ((2 - y) \sqrt[5]{{(2 - y)}^{3}})}{{(y - 2)}^{2}}$

Step 5.9

Apply the distributive property.

$\frac{\sqrt[3]{{(y - 2)}^{2}} (2 \sqrt[5]{{(2 - y)}^{3}} - y \sqrt[5]{{(2 - y)}^{3}})}{{(y - 2)}^{2}}$

Step 5.10

Factor $\sqrt[5]{{(2 - y)}^{3}}$ out of $2 \sqrt[5]{{(2 - y)}^{3}} - y \sqrt[5]{{(2 - y)}^{3}}$ .

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Step 5.10.1

Factor $\sqrt[5]{{(2 - y)}^{3}}$ out of $2 \sqrt[5]{{(2 - y)}^{3}}$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} (\sqrt[5]{{(2 - y)}^{3}} \cdot 2 - y \sqrt[5]{{(2 - y)}^{3}})}{{(y - 2)}^{2}}$

Step 5.10.2

Factor $\sqrt[5]{{(2 - y)}^{3}}$ out of $- y \sqrt[5]{{(2 - y)}^{3}}$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} (\sqrt[5]{{(2 - y)}^{3}} \cdot 2 + \sqrt[5]{{(2 - y)}^{3}} (- y))}{{(y - 2)}^{2}}$

Step 5.10.3

Factor $\sqrt[5]{{(2 - y)}^{3}}$ out of $\sqrt[5]{{(2 - y)}^{3}} \cdot 2 + \sqrt[5]{{(2 - y)}^{3}} (- y)$ .

$\frac{\sqrt[3]{{(y - 2)}^{2}} (\sqrt[5]{{(2 - y)}^{3}} (2 - y))}{{(y - 2)}^{2}}$

$\frac{\sqrt[3]{{(y - 2)}^{2}} \sqrt[5]{{(2 - y)}^{3}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.11

Combine exponents.

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Step 5.11.1

Rewrite the expression using the least common index of $15$ .

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Step 5.11.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{{(y - 2)}^{2}}$ as ${(y - 2)}^{\frac{2}{3}}$ .

$\frac{{(y - 2)}^{\frac{2}{3}} \sqrt[5]{{(2 - y)}^{3}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.11.1.2

Rewrite ${(y - 2)}^{\frac{2}{3}}$ as ${(y - 2)}^{\frac{10}{15}}$ .

$\frac{{(y - 2)}^{\frac{10}{15}} \sqrt[5]{{(2 - y)}^{3}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.11.1.3

Rewrite ${(y - 2)}^{\frac{10}{15}}$ as $\sqrt[15]{{(y - 2)}^{10}}$ .

$\frac{\sqrt[15]{{(y - 2)}^{10}} \sqrt[5]{{(2 - y)}^{3}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.11.1.4

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{{(2 - y)}^{3}}$ as ${(2 - y)}^{\frac{3}{5}}$ .

$\frac{\sqrt[15]{{(y - 2)}^{10}} {(2 - y)}^{\frac{3}{5}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.11.1.5

Rewrite ${(2 - y)}^{\frac{3}{5}}$ as ${(2 - y)}^{\frac{9}{15}}$ .

$\frac{\sqrt[15]{{(y - 2)}^{10}} {(2 - y)}^{\frac{9}{15}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.11.1.6

Rewrite ${(2 - y)}^{\frac{9}{15}}$ as $\sqrt[15]{{(2 - y)}^{9}}$ .

$\frac{\sqrt[15]{{(y - 2)}^{10}} \sqrt[15]{{(2 - y)}^{9}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.11.2

Combine using the product rule for radicals.

$\frac{\sqrt[15]{{(y - 2)}^{10} {(2 - y)}^{9}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.11.3

Factor $- 1$ out of $y$ .

$\frac{\sqrt[15]{{(- 1 (- y) - 2)}^{10} {(2 - y)}^{9}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.11.4

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{\sqrt[15]{{(- 1 (- y) - 1 (2))}^{10} {(2 - y)}^{9}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.11.5

Factor $- 1$ out of $- 1 (- y) - 1 (2)$ .

$\frac{\sqrt[15]{{(- 1 (- y + 2))}^{10} {(2 - y)}^{9}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.11.6

Apply the product rule to $- 1 (- y + 2)$ .

$\frac{\sqrt[15]{{(- 1)}^{10} {(- y + 2)}^{10} {(2 - y)}^{9}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.11.7

Raise $- 1$ to the power of $10$ .

$\frac{\sqrt[15]{1 {(- y + 2)}^{10} {(2 - y)}^{9}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.11.8

Multiply ${(- y + 2)}^{10}$ by $1$ .

$\frac{\sqrt[15]{{(- y + 2)}^{10} {(2 - y)}^{9}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.11.9

Reorder terms.

$\frac{\sqrt[15]{{(- y + 2)}^{10} {(- y + 2)}^{9}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.11.10

Multiply ${(- y + 2)}^{10}$ by ${(- y + 2)}^{9}$ by adding the exponents.

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Step 5.11.10.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt[15]{{(- y + 2)}^{10 + 9}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.11.10.2

Add $10$ and $9$ .

$\frac{\sqrt[15]{{(- y + 2)}^{19}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.12

Factor out ${(- y + 2)}^{15}$ .

$\frac{\sqrt[15]{{(- y + 2)}^{15} {(- y + 2)}^{4}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.13

Pull terms out from under the radical.

$\frac{(- y + 2) \sqrt[15]{{(- y + 2)}^{4}} (2 - y)}{{(y - 2)}^{2}}$

Step 5.14

Apply the distributive property.

$\frac{(- y \sqrt[15]{{(- y + 2)}^{4}} + 2 \sqrt[15]{{(- y + 2)}^{4}}) (2 - y)}{{(y - 2)}^{2}}$

Step 5.15

Factor $\sqrt[15]{{(- y + 2)}^{4}}$ out of $- y \sqrt[15]{{(- y + 2)}^{4}} + 2 \sqrt[15]{{(- y + 2)}^{4}}$ .

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Step 5.15.1

Factor $\sqrt[15]{{(- y + 2)}^{4}}$ out of $- y \sqrt[15]{{(- y + 2)}^{4}}$ .

$\frac{(\sqrt[15]{{(- y + 2)}^{4}} (- y) + 2 \sqrt[15]{{(- y + 2)}^{4}}) (2 - y)}{{(y - 2)}^{2}}$

Step 5.15.2

Factor $\sqrt[15]{{(- y + 2)}^{4}}$ out of $2 \sqrt[15]{{(- y + 2)}^{4}}$ .

$\frac{(\sqrt[15]{{(- y + 2)}^{4}} (- y) + \sqrt[15]{{(- y + 2)}^{4}} \cdot 2) (2 - y)}{{(y - 2)}^{2}}$

Step 5.15.3

Factor $\sqrt[15]{{(- y + 2)}^{4}}$ out of $\sqrt[15]{{(- y + 2)}^{4}} (- y) + \sqrt[15]{{(- y + 2)}^{4}} \cdot 2$ .

$\frac{\sqrt[15]{{(- y + 2)}^{4}} (- y + 2) (2 - y)}{{(y - 2)}^{2}}$

Step 6

Simplify the numerator.

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Step 6.1

Reorder terms.

$\frac{\sqrt[15]{{(- y + 2)}^{4}} (- y + 2) (- y + 2)}{{(y - 2)}^{2}}$

Step 6.2

Raise $- y + 2$ to the power of $1$ .

$\frac{\sqrt[15]{{(- y + 2)}^{4}} ({(- y + 2)}^{1} (- y + 2))}{{(y - 2)}^{2}}$

Step 6.3

Raise $- y + 2$ to the power of $1$ .

$\frac{\sqrt[15]{{(- y + 2)}^{4}} ({(- y + 2)}^{1} {(- y + 2)}^{1})}{{(y - 2)}^{2}}$

Step 6.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt[15]{{(- y + 2)}^{4}} {(- y + 2)}^{1 + 1}}{{(y - 2)}^{2}}$

Step 6.5

Add $1$ and $1$ .

$\frac{\sqrt[15]{{(- y + 2)}^{4}} {(- y + 2)}^{2}}{{(y - 2)}^{2}}$

Step 7

Cancel the common factor of ${(- y + 2)}^{2}$ and ${(y - 2)}^{2}$ .

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Step 7.1

Factor $- 1$ out of $- y$ .

$\frac{\sqrt[15]{{(- y + 2)}^{4}} {(- (y) + 2)}^{2}}{{(y - 2)}^{2}}$

Step 7.2

Rewrite $2$ as $- 1 (- 2)$ .

$\frac{\sqrt[15]{{(- y + 2)}^{4}} {(- (y) - 1 (- 2))}^{2}}{{(y - 2)}^{2}}$

Step 7.3

Factor $- 1$ out of $- (y) - 1 (- 2)$ .

$\frac{\sqrt[15]{{(- y + 2)}^{4}} {(- (y - 2))}^{2}}{{(y - 2)}^{2}}$

Step 7.4

Rewrite $- (y - 2)$ as $- 1 (y - 2)$ .

$\frac{\sqrt[15]{{(- y + 2)}^{4}} {(- 1 (y - 2))}^{2}}{{(y - 2)}^{2}}$

Step 7.5

Apply the product rule to $- 1 (y - 2)$ .

$\frac{\sqrt[15]{{(- y + 2)}^{4}} ({(- 1)}^{2} {(y - 2)}^{2})}{{(y - 2)}^{2}}$

Step 7.6

Raise $- 1$ to the power of $2$ .

$\frac{\sqrt[15]{{(- y + 2)}^{4}} (1 {(y - 2)}^{2})}{{(y - 2)}^{2}}$

Step 7.7

Multiply ${(y - 2)}^{2}$ by $1$ .

$\frac{\sqrt[15]{{(- y + 2)}^{4}} {(y - 2)}^{2}}{{(y - 2)}^{2}}$

Step 7.8

Cancel the common factor.

$\frac{\sqrt[15]{{(- y + 2)}^{4}} {(y - 2)}^{2}}{{(y - 2)}^{2}}$

Step 7.9

Divide $\sqrt[15]{{(- y + 2)}^{4}}$ by $1$ .

$\sqrt[15]{{(- y + 2)}^{4}}$