Basic Math Examples

$\frac{1000^{\frac{1}{3}}}{125^{\frac{1}{3}}} + 4^{3}$

Step 1

Simplify each term.

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Step 1.1

Simplify the numerator.

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Step 1.1.1

Rewrite $1000$ as $10^{3}$ .

$\frac{{(10^{3})}^{\frac{1}{3}}}{125^{\frac{1}{3}}} + 4^{3}$

Step 1.1.2

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

$\frac{10^{3 (\frac{1}{3})}}{125^{\frac{1}{3}}} + 4^{3}$

Step 1.1.3

Cancel the common factor of $3$ .

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Step 1.1.3.1

Cancel the common factor.

$\frac{10^{3 (\frac{1}{3})}}{125^{\frac{1}{3}}} + 4^{3}$

Step 1.1.3.2

Rewrite the expression.

$\frac{10^{1}}{125^{\frac{1}{3}}} + 4^{3}$

Step 1.1.4

Evaluate the exponent.

$\frac{10}{125^{\frac{1}{3}}} + 4^{3}$

Step 1.2

Simplify the denominator.

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Step 1.2.1

Rewrite $125$ as $5^{3}$ .

$\frac{10}{{(5^{3})}^{\frac{1}{3}}} + 4^{3}$

Step 1.2.2

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

$\frac{10}{5^{3 (\frac{1}{3})}} + 4^{3}$

Step 1.2.3

Cancel the common factor of $3$ .

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Step 1.2.3.1

Cancel the common factor.

$\frac{10}{5^{3 (\frac{1}{3})}} + 4^{3}$

Step 1.2.3.2

Rewrite the expression.

$\frac{10}{5^{1}} + 4^{3}$

Step 1.2.4

Evaluate the exponent.

$\frac{10}{5} + 4^{3}$

Step 1.3

Divide $10$ by $5$ .

$2 + 4^{3}$

Step 1.4

Raise $4$ to the power of $3$ .

$2 + 64$

Step 2

Add $2$ and $64$ .

$66$