Algebra Examples

$\frac{3 \cdot 2^{20} - 5 \cdot 2^{19}}{{(- 2^{6})}^{3}}$

Step 1

Simplify the numerator.

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Step 1.1

Raise $2$ to the power of $20$ .

$\frac{3 \cdot 1048576 - 5 \cdot 2^{19}}{{(- 2^{6})}^{3}}$

Step 1.2

Multiply $3$ by $1048576$ .

$\frac{3145728 - 5 \cdot 2^{19}}{{(- 2^{6})}^{3}}$

Step 1.3

Raise $2$ to the power of $19$ .

$\frac{3145728 - 5 \cdot 524288}{{(- 2^{6})}^{3}}$

Step 1.4

Multiply $- 5$ by $524288$ .

$\frac{3145728 - 2621440}{{(- 2^{6})}^{3}}$

Step 1.5

Subtract $2621440$ from $3145728$ .

$\frac{524288}{{(- 2^{6})}^{3}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $- 2^{6}$ .

$\frac{524288}{{(- 1)}^{3} {(2^{6})}^{3}}$

Step 2.2

Raise $- 1$ to the power of $3$ .

$\frac{524288}{- {(2^{6})}^{3}}$

Step 2.3

Multiply the exponents in ${(2^{6})}^{3}$ .

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Step 2.3.1

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

$\frac{524288}{- 2^{6 \cdot 3}}$

Step 2.3.2

Multiply $6$ by $3$ .

$\frac{524288}{- 2^{18}}$

Step 2.4

Raise $2$ to the power of $18$ .

$\frac{524288}{- 1 \cdot 262144}$

Step 3

Simplify the expression.

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Step 3.1

Multiply $- 1$ by $262144$ .

$\frac{524288}{- 262144}$

Step 3.2

Divide $524288$ by $- 262144$ .

$- 2$