Basic Math Examples

${({(6^{8} \cdot 6^{5} \div 6^{10})}^{2} \div 6^{5})}^{3} \div 3^{3} + 2^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite the division as a fraction.

$\frac{{({(6^{8} \cdot 6^{5} \div 6^{10})}^{2} \div 6^{5})}^{3}}{3^{3}} + 2^{2}$

Step 1.2

Cancel the common factor of $6^{8}$ and $6^{10}$ .

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Step 1.2.1

Factor $6^{8}$ out of $6^{8} \cdot 6^{5}$ .

$\frac{{({(6^{8} (6^{5}) \div 6^{10})}^{2} \div 6^{5})}^{3}}{3^{3}} + 2^{2}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $6^{8}$ out of $6^{10}$ .

$\frac{{({(6^{8} (6^{5}) \div 6^{8} \cdot 6^{2})}^{2} \div 6^{5})}^{3}}{3^{3}} + 2^{2}$

Step 1.2.2.2

Cancel the common factor.

$\frac{{({(6^{8} \cdot 6^{5} \div 6^{8} \cdot 6^{2})}^{2} \div 6^{5})}^{3}}{3^{3}} + 2^{2}$

Step 1.2.2.3

Rewrite the expression.

$\frac{{({(\frac{6^{5}}{6^{2}})}^{2} \div 6^{5})}^{3}}{3^{3}} + 2^{2}$

Step 1.3

Cancel the common factor of $6^{5}$ and $6^{2}$ .

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Step 1.3.1

Factor $6^{2}$ out of $6^{5}$ .

$\frac{{({(\frac{6^{2} \cdot 6^{3}}{6^{2}})}^{2} \div 6^{5})}^{3}}{3^{3}} + 2^{2}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Multiply by $1$ .

$\frac{{({(\frac{6^{2} \cdot 6^{3}}{6^{2} \cdot 1})}^{2} \div 6^{5})}^{3}}{3^{3}} + 2^{2}$

Step 1.3.2.2

Cancel the common factor.

$\frac{{({(\frac{6^{2} \cdot 6^{3}}{6^{2} \cdot 1})}^{2} \div 6^{5})}^{3}}{3^{3}} + 2^{2}$

Step 1.3.2.3

Rewrite the expression.

$\frac{{({(\frac{6^{3}}{1})}^{2} \div 6^{5})}^{3}}{3^{3}} + 2^{2}$

Step 1.3.2.4

Divide $6^{3}$ by $1$ .

$\frac{{({(6^{3})}^{2} \div 6^{5})}^{3}}{3^{3}} + 2^{2}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

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

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Step 1.4.1.1

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

$\frac{{(6^{3 \cdot 2} \div 6^{5})}^{3}}{3^{3}} + 2^{2}$

Step 1.4.1.2

Multiply $3$ by $2$ .

$\frac{{(6^{6} \div 6^{5})}^{3}}{3^{3}} + 2^{2}$

Step 1.4.2

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

$\frac{{(46656 \div 6^{5})}^{3}}{3^{3}} + 2^{2}$

Step 1.5

Raise $6$ to the power of $5$ .

$\frac{{(46656 \div 7776)}^{3}}{3^{3}} + 2^{2}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Divide $46656$ by $7776$ .

$\frac{6^{3}}{3^{3}} + 2^{2}$

Step 1.6.2

Raise $6$ to the power of $3$ .

$\frac{216}{3^{3}} + 2^{2}$

Step 1.7

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

$\frac{216}{27} + 2^{2}$

Step 1.8

Divide $216$ by $27$ .

$8 + 2^{2}$

Step 1.9

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

$8 + 4$

Step 2

Add $8$ and $4$ .

$12$