Algebra Examples

$\frac{(4 \cdot 3^{22} + 7 \cdot 3^{21}) \cdot 57}{{(19 \cdot 27^{4})}^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Raise $3$ to the power of $22$ .

$\frac{(4 \cdot 31381059609 + 7 \cdot 3^{21}) \cdot 57}{{(19 \cdot 27^{4})}^{2}}$

Step 1.2

Multiply $4$ by $31381059609$ .

$\frac{(125524238436 + 7 \cdot 3^{21}) \cdot 57}{{(19 \cdot 27^{4})}^{2}}$

Step 1.3

Raise $3$ to the power of $21$ .

$\frac{(125524238436 + 7 \cdot 10460353203) \cdot 57}{{(19 \cdot 27^{4})}^{2}}$

Step 1.4

Multiply $7$ by $10460353203$ .

$\frac{(125524238436 + 73222472421) \cdot 57}{{(19 \cdot 27^{4})}^{2}}$

Step 1.5

Add $125524238436$ and $73222472421$ .

$\frac{198746710857 \cdot 57}{{(19 \cdot 27^{4})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $19 \cdot 27^{4}$ .

$\frac{198746710857 \cdot 57}{19^{2} \cdot {(27^{4})}^{2}}$

Step 2.2

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

$\frac{198746710857 \cdot 57}{361 \cdot {(27^{4})}^{2}}$

Step 2.3

Multiply the exponents in ${(27^{4})}^{2}$ .

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Step 2.3.1

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

$\frac{198746710857 \cdot 57}{361 \cdot 27^{4 \cdot 2}}$

Step 2.3.2

Multiply $4$ by $2$ .

$\frac{198746710857 \cdot 57}{361 \cdot 27^{8}}$

Step 2.4

Raise $27$ to the power of $8$ .

$\frac{198746710857 \cdot 57}{361 \cdot 282429536481}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply $198746710857$ by $57$ .

$\frac{11328562518849}{361 \cdot 282429536481}$

Step 3.2

Multiply $361$ by $282429536481$ .

$\frac{11328562518849}{101957062669641}$

Step 3.3

Cancel the common factor of $11328562518849$ and $101957062669641$ .

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Step 3.3.1

Factor $11328562518849$ out of $11328562518849$ .

$\frac{11328562518849 (1)}{101957062669641}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $11328562518849$ out of $101957062669641$ .

$\frac{11328562518849 \cdot 1}{11328562518849 \cdot 9}$

Step 3.3.2.2

Cancel the common factor.

$\frac{11328562518849 \cdot 1}{11328562518849 \cdot 9}$

Step 3.3.2.3

Rewrite the expression.

$\frac{1}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{9}$

Decimal Form:

$0.\overline{1}$