Basic Math Examples

${(\frac{1}{6})}^{4} \cdot {(\frac{5}{6})}^{4} \cdot (70)$

Step 1

Combine fractions.

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Step 1.1

Apply the product rule to $\frac{1}{6}$ .

$\frac{1^{4}}{6^{4}} \cdot {(\frac{5}{6})}^{4} \cdot 70$

Step 1.2

Simplify the expression.

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Step 1.2.1

One to any power is one.

$\frac{1}{6^{4}} \cdot {(\frac{5}{6})}^{4} \cdot 70$

Step 1.2.2

Raise $6$ to the power of $4$ .

$\frac{1}{1296} \cdot {(\frac{5}{6})}^{4} \cdot 70$

Step 1.2.3

Apply the product rule to $\frac{5}{6}$ .

$\frac{1}{1296} \cdot \frac{5^{4}}{6^{4}} \cdot 70$

Step 1.3

Combine.

$\frac{1 \cdot 5^{4}}{1296 \cdot 6^{4}} \cdot 70$

Step 1.4

Multiply $5^{4}$ by $1$ .

$\frac{5^{4}}{1296 \cdot 6^{4}} \cdot 70$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $1296$ as $6^{4}$ .

$\frac{5^{4}}{6^{4} \cdot 6^{4}} \cdot 70$

Step 2.2

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

$\frac{5^{4}}{6^{4 + 4}} \cdot 70$

Step 2.3

Add $4$ and $4$ .

$\frac{5^{4}}{6^{8}} \cdot 70$

Step 3

Simplify terms.

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Step 3.1

Raise $5$ to the power of $4$ .

$\frac{625}{6^{8}} \cdot 70$

Step 3.2

Raise $6$ to the power of $8$ .

$\frac{625}{1679616} \cdot 70$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Factor $2$ out of $1679616$ .

$\frac{625}{2 (839808)} \cdot 70$

Step 3.3.2

Factor $2$ out of $70$ .

$\frac{625}{2 \cdot 839808} \cdot (2 \cdot 35)$

Step 3.3.3

Cancel the common factor.

$\frac{625}{2 \cdot 839808} \cdot (2 \cdot 35)$

Step 3.3.4

Rewrite the expression.

$\frac{625}{839808} \cdot 35$

Step 3.4

Combine $\frac{625}{839808}$ and $35$ .

$\frac{625 \cdot 35}{839808}$

Step 3.5

Multiply $625$ by $35$ .

$\frac{21875}{839808}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{21875}{839808}$

Decimal Form:

$0.02604762 \dots$