Basic Math Examples

${(\frac{4 \sqrt{11}}{15})}^{2} - {(\frac{7}{15})}^{2}$

Step 1

Simplify each term.

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Step 1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.1

Apply the product rule to $\frac{4 \sqrt{11}}{15}$ .

$\frac{{(4 \sqrt{11})}^{2}}{15^{2}} - {(\frac{7}{15})}^{2}$

Step 1.1.2

Apply the product rule to $4 \sqrt{11}$ .

$\frac{4^{2} {\sqrt{11}}^{2}}{15^{2}} - {(\frac{7}{15})}^{2}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

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

$\frac{16 {\sqrt{11}}^{2}}{15^{2}} - {(\frac{7}{15})}^{2}$

Step 1.2.2

Rewrite ${\sqrt{11}}^{2}$ as $11$ .

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Step 1.2.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{11}$ as $11^{\frac{1}{2}}$ .

$\frac{16 {(11^{\frac{1}{2}})}^{2}}{15^{2}} - {(\frac{7}{15})}^{2}$

Step 1.2.2.2

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

$\frac{16 \cdot 11^{\frac{1}{2} \cdot 2}}{15^{2}} - {(\frac{7}{15})}^{2}$

Step 1.2.2.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{16 \cdot 11^{\frac{2}{2}}}{15^{2}} - {(\frac{7}{15})}^{2}$

Step 1.2.2.4

Cancel the common factor of $2$ .

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Step 1.2.2.4.1

Cancel the common factor.

$\frac{16 \cdot 11^{\frac{2}{2}}}{15^{2}} - {(\frac{7}{15})}^{2}$

Step 1.2.2.4.2

Rewrite the expression.

$\frac{16 \cdot 11^{1}}{15^{2}} - {(\frac{7}{15})}^{2}$

Step 1.2.2.5

Evaluate the exponent.

$\frac{16 \cdot 11}{15^{2}} - {(\frac{7}{15})}^{2}$

Step 1.3

Raise $15$ to the power of $2$ .

$\frac{16 \cdot 11}{225} - {(\frac{7}{15})}^{2}$

Step 1.4

Multiply $16$ by $11$ .

$\frac{176}{225} - {(\frac{7}{15})}^{2}$

Step 1.5

Apply the product rule to $\frac{7}{15}$ .

$\frac{176}{225} - \frac{7^{2}}{15^{2}}$

Step 1.6

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

$\frac{176}{225} - \frac{49}{15^{2}}$

Step 1.7

Raise $15$ to the power of $2$ .

$\frac{176}{225} - \frac{49}{225}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{176 - 49}{225}$

Step 2.2

Subtract $49$ from $176$ .

$\frac{127}{225}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{127}{225}$

Decimal Form:

$0.56\overline{4}$