Algebra Examples

$\frac{(2^{- 4}) (4^{3}) (3^{3})}{4}$

Step 1

Move $2^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4^{3} \cdot 3^{3}}{4 \cdot 2^{4}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $4$ as $2^{2}$ .

$\frac{4^{3} \cdot 3^{3}}{2^{2} \cdot 2^{4}}$

Step 2.2

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

$\frac{4^{3} \cdot 3^{3}}{2^{2 + 4}}$

Step 2.3

Add $2$ and $4$ .

$\frac{4^{3} \cdot 3^{3}}{2^{6}}$

Step 3

Simplify the numerator.

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Step 3.1

Raise $4$ to the power of $3$ .

$\frac{64 \cdot 3^{3}}{2^{6}}$

Step 3.2

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

$\frac{64 \cdot 27}{2^{6}}$

Step 4

Simplify the expression.

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Step 4.1

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

$\frac{64 \cdot 27}{64}$

Step 4.2

Multiply $64$ by $27$ .

$\frac{1728}{64}$

Step 4.3

Divide $1728$ by $64$ .

$27$