Algebra Examples

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

Step 1

Cancel the common factor of $2^{m}$ and $2^{- 3}$ .

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Step 1.1

Factor $2^{- 3}$ out of $2^{m}$ .

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Multiply by $1$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 1.2.4

Divide $2^{m + 3}$ by $1$ .

${(2^{m + 3})}^{2}$

Step 2

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

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Step 2.1

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

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Move $2$ to the left of $m$ .

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

Step 2.4

Multiply $3$ by $2$ .

$2^{2 m + 6}$