Algebra Examples

$2^{4} \cdot 2^{5} - {(2^{2})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Multiply $2^{4}$ by $2^{5}$ by adding the exponents.

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Step 1.1.1

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

$2^{4 + 5} - {(2^{2})}^{2}$

Step 1.1.2

Add $4$ and $5$ .

$2^{9} - {(2^{2})}^{2}$

Step 1.2

Raise $2$ to the power of $9$ .

$512 - {(2^{2})}^{2}$

Step 1.3

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

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Step 1.3.1

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

$512 - 2^{2 \cdot 2}$

Step 1.3.2

Multiply $2$ by $2$ .

$512 - 2^{4}$

Step 1.4

Raise $2$ to the power of $4$ .

$512 - 1 \cdot 16$

Step 1.5

Multiply $- 1$ by $16$ .

$512 - 16$

Step 2

Subtract $16$ from $512$ .

$496$