Basic Math Examples

$\frac{81^{\frac{1}{3}}}{375^{\frac{1}{3}}} \cdot \frac{16^{\frac{1}{4}}}{375^{\frac{1}{3}}}$

Step 1

Combine.

$\frac{81^{\frac{1}{3}} \cdot 16^{\frac{1}{4}}}{375^{\frac{1}{3}} \cdot 375^{\frac{1}{3}}}$

Step 2

Multiply $375^{\frac{1}{3}}$ by $375^{\frac{1}{3}}$ by adding the exponents.

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Step 2.1

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

$\frac{81^{\frac{1}{3}} \cdot 16^{\frac{1}{4}}}{375^{\frac{1}{3} + \frac{1}{3}}}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{81^{\frac{1}{3}} \cdot 16^{\frac{1}{4}}}{375^{\frac{1 + 1}{3}}}$

Step 2.3

Add $1$ and $1$ .

$\frac{81^{\frac{1}{3}} \cdot 16^{\frac{1}{4}}}{375^{\frac{2}{3}}}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $16$ as $2^{4}$ .

$\frac{81^{\frac{1}{3}} \cdot {(2^{4})}^{\frac{1}{4}}}{375^{\frac{2}{3}}}$

Step 3.2

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

$\frac{81^{\frac{1}{3}} \cdot 2^{4 (\frac{1}{4})}}{375^{\frac{2}{3}}}$

Step 3.3

Cancel the common factor of $4$ .

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Step 3.3.1

Cancel the common factor.

$\frac{81^{\frac{1}{3}} \cdot 2^{4 (\frac{1}{4})}}{375^{\frac{2}{3}}}$

Step 3.3.2

Rewrite the expression.

$\frac{81^{\frac{1}{3}} \cdot 2^{1}}{375^{\frac{2}{3}}}$

Step 3.4

Evaluate the exponent.

$\frac{81^{\frac{1}{3}} \cdot 2}{375^{\frac{2}{3}}}$

Step 4

Move $2$ to the left of $81^{\frac{1}{3}}$ .

$\frac{2 \cdot 81^{\frac{1}{3}}}{375^{\frac{2}{3}}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \cdot 81^{\frac{1}{3}}}{375^{\frac{2}{3}}}$

Decimal Form:

$0.16640670 \dots$