Algebra Examples

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

Step 1

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

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Step 1.1

Multiply $m$ by $m^{- 2}$ .

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Step 1.1.1

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

${(m^{1} \cdot m^{- 2} \cdot m^{\frac{5}{3}})}^{2}$

Step 1.1.2

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

${(m^{1 - 2} \cdot m^{\frac{5}{3}})}^{2}$

Step 1.2

Subtract $2$ from $1$ .

${(m^{- 1} \cdot m^{\frac{5}{3}})}^{2}$

Step 2

Multiply $m^{- 1}$ by $m^{\frac{5}{3}}$ by adding the exponents.

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Step 2.1

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

${(m^{- 1 + \frac{5}{3}})}^{2}$

Step 2.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

${(m^{- 1 \cdot \frac{3}{3} + \frac{5}{3}})}^{2}$

Step 2.3

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

${(m^{\frac{- 1 \cdot 3}{3} + \frac{5}{3}})}^{2}$

Step 2.4

Combine the numerators over the common denominator.

${(m^{\frac{- 1 \cdot 3 + 5}{3}})}^{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 1$ by $3$ .

${(m^{\frac{- 3 + 5}{3}})}^{2}$

Step 2.5.2

Add $- 3$ and $5$ .

${(m^{\frac{2}{3}})}^{2}$

Step 3

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

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Step 3.1

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

$m^{\frac{2}{3} \cdot 2}$

Step 3.2

Multiply $\frac{2}{3} \cdot 2$ .

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Step 3.2.1

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

$m^{\frac{2 \cdot 2}{3}}$

Step 3.2.2

Multiply $2$ by $2$ .

$m^{\frac{4}{3}}$