Basic Math Examples

$\frac{8^{16}}{{(2 \cdot 2^{2} \cdot 4^{10})}^{2}}$

Step 1

Raise $8$ to the power of $16$ .

$\frac{281474976710656}{{(2 \cdot 2^{2} \cdot 4^{10})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $2 \cdot 2^{2} \cdot 4^{10}$ .

$\frac{281474976710656}{{(2 \cdot 2^{2})}^{2} \cdot {(4^{10})}^{2}}$

Step 2.2

Multiply $2$ by $2^{2}$ by adding the exponents.

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Step 2.2.1

Multiply $2$ by $2^{2}$ .

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Step 2.2.1.1

Raise $2$ to the power of $1$ .

$\frac{281474976710656}{{(2^{1} \cdot 2^{2})}^{2} \cdot {(4^{10})}^{2}}$

Step 2.2.1.2

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

$\frac{281474976710656}{{(2^{1 + 2})}^{2} \cdot {(4^{10})}^{2}}$

Step 2.2.2

Add $1$ and $2$ .

$\frac{281474976710656}{{(2^{3})}^{2} \cdot {(4^{10})}^{2}}$

Step 2.3

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

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Step 2.3.1

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

$\frac{281474976710656}{2^{3 \cdot 2} \cdot {(4^{10})}^{2}}$

Step 2.3.2

Multiply $3$ by $2$ .

$\frac{281474976710656}{2^{6} \cdot {(4^{10})}^{2}}$

Step 2.4

Raise $2$ to the power of $6$ .

$\frac{281474976710656}{64 \cdot {(4^{10})}^{2}}$

Step 2.5

Multiply the exponents in ${(4^{10})}^{2}$ .

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Step 2.5.1

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

$\frac{281474976710656}{64 \cdot 4^{10 \cdot 2}}$

Step 2.5.2

Multiply $10$ by $2$ .

$\frac{281474976710656}{64 \cdot 4^{20}}$

Step 2.6

Raise $4$ to the power of $20$ .

$\frac{281474976710656}{64 \cdot 1099511627776}$

Step 3

Simplify the expression.

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Step 3.1

Multiply $64$ by $1099511627776$ .

$\frac{281474976710656}{70368744177664}$

Step 3.2

Divide $281474976710656$ by $70368744177664$ .

$4$