Algebra Examples

${(\frac{m^{7} \cdot m}{z^{2} \cdot m^{3}})}^{2}$

Step 1

Multiply $m^{7}$ by $m$ by adding the exponents.

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Step 1.1

Multiply $m^{7}$ by $m$ .

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Step 1.1.1

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

${(\frac{m^{7} \cdot m^{1}}{z^{2} \cdot m^{3}})}^{2}$

Step 1.1.2

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

${(\frac{m^{7 + 1}}{z^{2} \cdot m^{3}})}^{2}$

Step 1.2

Add $7$ and $1$ .

${(\frac{m^{8}}{z^{2} \cdot m^{3}})}^{2}$

Step 2

Cancel the common factor of $m^{8}$ and $m^{3}$ .

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Step 2.1

Factor $m^{3}$ out of $m^{8}$ .

${(\frac{m^{3} m^{5}}{z^{2} \cdot m^{3}})}^{2}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $m^{3}$ out of $z^{2} \cdot m^{3}$ .

${(\frac{m^{3} m^{5}}{m^{3} \cdot z^{2}})}^{2}$

Step 2.2.2

Cancel the common factor.

${(\frac{m^{3} m^{5}}{m^{3} \cdot z^{2}})}^{2}$

Step 2.2.3

Rewrite the expression.

${(\frac{m^{5}}{z^{2}})}^{2}$

Step 3

Apply basic rules of exponents.

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Step 3.1

Apply the product rule to $\frac{m^{5}}{z^{2}}$ .

$\frac{{(m^{5})}^{2}}{{(z^{2})}^{2}}$

Step 3.2

Multiply the exponents in ${(m^{5})}^{2}$ .

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Step 3.2.1

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

$\frac{m^{5 \cdot 2}}{{(z^{2})}^{2}}$

Step 3.2.2

Multiply $5$ by $2$ .

$\frac{m^{10}}{{(z^{2})}^{2}}$

Step 3.3

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

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Step 3.3.1

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

$\frac{m^{10}}{z^{2 \cdot 2}}$

Step 3.3.2

Multiply $2$ by $2$ .

$\frac{m^{10}}{z^{4}}$