Basic Math Examples

${(\frac{- 4}{7})}^{2} + 3$

Step 1

Simplify each term.

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Step 1.1

Move the negative in front of the fraction.

${(- \frac{4}{7})}^{2} + 3$

Step 1.2

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

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Step 1.2.1

Apply the product rule to $- \frac{4}{7}$ .

${(- 1)}^{2} {(\frac{4}{7})}^{2} + 3$

Step 1.2.2

Apply the product rule to $\frac{4}{7}$ .

${(- 1)}^{2} \frac{4^{2}}{7^{2}} + 3$

Step 1.3

Raise $- 1$ to the power of $2$ .

$1 \frac{4^{2}}{7^{2}} + 3$

Step 1.4

Multiply $\frac{4^{2}}{7^{2}}$ by $1$ .

$\frac{4^{2}}{7^{2}} + 3$

Step 1.5

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

$\frac{16}{7^{2}} + 3$

Step 1.6

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

$\frac{16}{49} + 3$

Step 2

To write $3$ as a fraction with a common denominator, multiply by $\frac{49}{49}$ .

$\frac{16}{49} + 3 \cdot \frac{49}{49}$

Step 3

Combine $3$ and $\frac{49}{49}$ .

$\frac{16}{49} + \frac{3 \cdot 49}{49}$

Step 4

Combine the numerators over the common denominator.

$\frac{16 + 3 \cdot 49}{49}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $49$ .

$\frac{16 + 147}{49}$

Step 5.2

Add $16$ and $147$ .

$\frac{163}{49}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{163}{49}$

Decimal Form:

$3.32653061 \dots$

Mixed Number Form:

$3 \frac{16}{49}$