Basic Math Examples

${(\frac{2}{9})}^{2} \cdot {(\frac{9}{7})}^{2}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $\frac{2}{9}$ .

$\frac{2^{2}}{9^{2}} \cdot {(\frac{9}{7})}^{2}$

Step 1.2

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

$\frac{4}{9^{2}} \cdot {(\frac{9}{7})}^{2}$

Step 1.3

Raise $9$ to the power of $2$ .

$\frac{4}{81} \cdot {(\frac{9}{7})}^{2}$

Step 1.4

Apply the product rule to $\frac{9}{7}$ .

$\frac{4}{81} \cdot \frac{9^{2}}{7^{2}}$

$\frac{4}{81} \cdot \frac{9^{2}}{7^{2}}$

Step 2

Combine.

$\frac{4 \cdot 9^{2}}{81 \cdot 7^{2}}$

Step 3

Simplify the expression.

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Step 3.1

Raise $9$ to the power of $2$ .

$\frac{4 \cdot 81}{81 \cdot 7^{2}}$

Step 3.2

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

$\frac{4 \cdot 81}{81 \cdot 49}$

Step 3.3

Multiply $4$ by $81$ .

$\frac{324}{81 \cdot 49}$

Step 3.4

Multiply $81$ by $49$ .

$\frac{324}{3969}$

$\frac{324}{3969}$

Step 4

Cancel the common factor of $324$ and $3969$ .

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Step 4.1

Factor $81$ out of $324$ .

$\frac{81 (4)}{3969}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $81$ out of $3969$ .

$\frac{81 \cdot 4}{81 \cdot 49}$

Step 4.2.2

Cancel the common factor.

$\frac{81 \cdot 4}{81 \cdot 49}$

Step 4.2.3

Rewrite the expression.

$\frac{4}{49}$

$\frac{4}{49}$

$\frac{4}{49}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{49}$

Decimal Form:

$0.08163265 \dots$

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