Basic Math Examples

$\frac{{({(2)}^{5})}^{9}}{2^{50}}$

Step 1

Simplify the numerator.

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Step 1.1

Multiply the exponents in ${(2^{5})}^{9}$ .

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Step 1.1.1

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

$\frac{2^{5 \cdot 9}}{2^{50}}$

Step 1.1.2

Multiply $5$ by $9$ .

$\frac{2^{45}}{2^{50}}$

Step 1.2

Raise $2$ to the power of $45$ .

$\frac{35184372088832}{2^{50}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Raise $2$ to the power of $50$ .

$\frac{35184372088832}{1125899906842620}$

Step 2.2

Cancel the common factor of $35184372088832$ and $1125899906842620$ .

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Step 2.2.1

Factor $4$ out of $35184372088832$ .

$\frac{4 (8796093022208)}{1125899906842620}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $4$ out of $1125899906842620$ .

$\frac{4 \cdot 8796093022208}{4 \cdot 281474976710655}$

Step 2.2.2.2

Cancel the common factor.

$\frac{4 \cdot 8796093022208}{4 \cdot 281474976710655}$

Step 2.2.2.3

Rewrite the expression.

$\frac{8796093022208}{281474976710655}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{8796093022208}{281474976710655}$

Decimal Form:

$0.03125000 \dots$