Basic Math Examples

$4^{3} \cdot 2 \div {(6 - 4)}^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{4^{3} \cdot 2}{{(6 - 4)}^{2}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $4$ as $2^{2}$ .

$\frac{{(2^{2})}^{3} \cdot 2}{{(6 - 4)}^{2}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{2^{2 \cdot 3} \cdot 2}{{(6 - 4)}^{2}}$

Step 2.2.2

Multiply $2$ by $3$ .

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

Step 2.3

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

$\frac{2^{6 + 1}}{{(6 - 4)}^{2}}$

Step 2.4

Add $6$ and $1$ .

$\frac{2^{7}}{{(6 - 4)}^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

Subtract $4$ from $6$ .

$\frac{2^{7}}{2^{2}}$

Step 3.2

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

$\frac{2^{7}}{4}$

Step 4

Simplify the expression.

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Step 4.1

Raise $2$ to the power of $7$ .

$\frac{128}{4}$

Step 4.2

Divide $128$ by $4$ .

$32$