Algebra Examples

${(m^{5} n^{3})}^{7} \cdot m^{2} n$

Step 1

Apply the product rule to $m^{5} n^{3}$ .

${(m^{5})}^{7} {(n^{3})}^{7} \cdot (m^{2} n)$

Step 2

Multiply the exponents in ${(m^{5})}^{7}$ .

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Step 2.1

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

$m^{5 \cdot 7} {(n^{3})}^{7} \cdot (m^{2} n)$

Step 2.2

Multiply $5$ by $7$ .

$m^{35} {(n^{3})}^{7} \cdot (m^{2} n)$

Step 3

Multiply $m^{35}$ by $m^{2}$ by adding the exponents.

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Step 3.1

Move $m^{2}$ .

$m^{2} m^{35} {(n^{3})}^{7} \cdot n$

Step 3.2

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

$m^{2 + 35} {(n^{3})}^{7} \cdot n$

Step 3.3

Add $2$ and $35$ .

$m^{37} {(n^{3})}^{7} \cdot n$

Step 4

Multiply the exponents in ${(n^{3})}^{7}$ .

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Step 4.1

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

$m^{37} n^{3 \cdot 7} \cdot n$

Step 4.2

Multiply $3$ by $7$ .

$m^{37} n^{21} \cdot n$

Step 5

Multiply $n^{21}$ by $n$ by adding the exponents.

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Step 5.1

Move $n$ .

$m^{37} (n \cdot n^{21})$

Step 5.2

Multiply $n$ by $n^{21}$ .

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Step 5.2.1

Raise $n$ to the power of $1$ .

$m^{37} (n^{1} n^{21})$

Step 5.2.2

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

$m^{37} n^{1 + 21}$

Step 5.3

Add $1$ and $21$ .

$m^{37} n^{22}$