Basic Math Examples

${(\frac{2}{3})}^{4} \cdot {(\frac{81}{100})}^{2}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $\frac{2}{3}$ .

$\frac{2^{4}}{3^{4}} \cdot {(\frac{81}{100})}^{2}$

Step 1.2

Raise $2$ to the power of $4$ .

$\frac{16}{3^{4}} \cdot {(\frac{81}{100})}^{2}$

Step 1.3

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

$\frac{16}{81} \cdot {(\frac{81}{100})}^{2}$

Step 1.4

Apply the product rule to $\frac{81}{100}$ .

$\frac{16}{81} \cdot \frac{81^{2}}{100^{2}}$

$\frac{16}{81} \cdot \frac{81^{2}}{100^{2}}$

Step 2

Combine.

$\frac{16 \cdot 81^{2}}{81 \cdot 100^{2}}$

Step 3

Cancel the common factor of $81^{2}$ and $81$ .

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Step 3.1

Factor $81$ out of $16 \cdot 81^{2}$ .

$\frac{81 (16 \cdot 81)}{81 \cdot 100^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $81$ out of $81 \cdot 100^{2}$ .

$\frac{81 (16 \cdot 81)}{81 (100^{2})}$

Step 3.2.2

Cancel the common factor.

$\frac{81 (16 \cdot 81)}{81 \cdot 100^{2}}$

Step 3.2.3

Rewrite the expression.

$\frac{16 \cdot 81}{100^{2}}$

$\frac{16 \cdot 81}{100^{2}}$

$\frac{16 \cdot 81}{100^{2}}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $16$ by $81$ .

$\frac{1296}{100^{2}}$

Step 4.2

Raise $100$ to the power of $2$ .

$\frac{1296}{10000}$

$\frac{1296}{10000}$

Step 5

Cancel the common factor of $1296$ and $10000$ .

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Step 5.1

Factor $16$ out of $1296$ .

$\frac{16 (81)}{10000}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $16$ out of $10000$ .

$\frac{16 \cdot 81}{16 \cdot 625}$

Step 5.2.2

Cancel the common factor.

$\frac{16 \cdot 81}{16 \cdot 625}$

Step 5.2.3

Rewrite the expression.

$\frac{81}{625}$

$\frac{81}{625}$

$\frac{81}{625}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{81}{625}$

Decimal Form:

$0.1296$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$