Basic Math Examples

$- {(\frac{2}{5})}^{2} \cdot {(\frac{5}{7})}^{2} \cdot \frac{49}{5} + {(- \frac{4}{5})}^{3} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{2}{5}$ .

$- \frac{2^{2}}{5^{2}} \cdot {(\frac{5}{7})}^{2} \cdot \frac{49}{5} + {(- \frac{4}{5})}^{3} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.2

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

$- \frac{4}{5^{2}} \cdot {(\frac{5}{7})}^{2} \cdot \frac{49}{5} + {(- \frac{4}{5})}^{3} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.3

Raise $5$ to the power of $2$ .

$- \frac{4}{25} \cdot {(\frac{5}{7})}^{2} \cdot \frac{49}{5} + {(- \frac{4}{5})}^{3} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.4

Apply the product rule to $\frac{5}{7}$ .

$- \frac{4}{25} \cdot \frac{5^{2}}{7^{2}} \cdot \frac{49}{5} + {(- \frac{4}{5})}^{3} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.5

Raise $5$ to the power of $2$ .

$- \frac{4}{25} \cdot \frac{25}{7^{2}} \cdot \frac{49}{5} + {(- \frac{4}{5})}^{3} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.6

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

$- \frac{4}{25} \cdot \frac{25}{49} \cdot \frac{49}{5} + {(- \frac{4}{5})}^{3} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.7

Cancel the common factor of $25$ .

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Step 1.7.1

Move the leading negative in $- \frac{4}{25}$ into the numerator.

$\frac{- 4}{25} \cdot \frac{25}{49} \cdot \frac{49}{5} + {(- \frac{4}{5})}^{3} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.7.2

Cancel the common factor.

$\frac{- 4}{25} \cdot \frac{25}{49} \cdot \frac{49}{5} + {(- \frac{4}{5})}^{3} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.7.3

Rewrite the expression.

$- 4 \cdot \frac{1}{49} \cdot \frac{49}{5} + {(- \frac{4}{5})}^{3} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.8

Combine $- 4$ and $\frac{1}{49}$ .

$\frac{- 4}{49} \cdot \frac{49}{5} + {(- \frac{4}{5})}^{3} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.9

Cancel the common factor of $49$ .

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Step 1.9.1

Cancel the common factor.

$\frac{- 4}{49} \cdot \frac{49}{5} + {(- \frac{4}{5})}^{3} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.9.2

Rewrite the expression.

$- 4 \cdot \frac{1}{5} + {(- \frac{4}{5})}^{3} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.10

Combine $- 4$ and $\frac{1}{5}$ .

$\frac{- 4}{5} + {(- \frac{4}{5})}^{3} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.11

Move the negative in front of the fraction.

$- \frac{4}{5} + {(- \frac{4}{5})}^{3} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.12

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

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Step 1.12.1

Apply the product rule to $- \frac{4}{5}$ .

$- \frac{4}{5} + {(- 1)}^{3} {(\frac{4}{5})}^{3} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.12.2

Apply the product rule to $\frac{4}{5}$ .

$- \frac{4}{5} + {(- 1)}^{3} \frac{4^{3}}{5^{3}} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.13

Raise $- 1$ to the power of $3$ .

$- \frac{4}{5} - \frac{4^{3}}{5^{3}} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.14

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

$- \frac{4}{5} - \frac{64}{5^{3}} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.15

Raise $5$ to the power of $3$ .

$- \frac{4}{5} - \frac{64}{125} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.16

Cancel the common factor of $4$ .

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Step 1.16.1

Move the leading negative in $- \frac{64}{125}$ into the numerator.

$- \frac{4}{5} + \frac{- 64}{125} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.16.2

Factor $4$ out of $- 64$ .

$- \frac{4}{5} + \frac{4 (- 16)}{125} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.16.3

Cancel the common factor.

$- \frac{4}{5} + \frac{4 \cdot - 16}{125} \cdot \frac{5}{4} \cdot \frac{3}{7}$

Step 1.16.4

Rewrite the expression.

$- \frac{4}{5} + \frac{- 16}{125} \cdot 5 \cdot \frac{3}{7}$

Step 1.17

Cancel the common factor of $5$ .

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Step 1.17.1

Factor $5$ out of $125$ .

$- \frac{4}{5} + \frac{- 16}{5 (25)} \cdot 5 \cdot \frac{3}{7}$

Step 1.17.2

Cancel the common factor.

$- \frac{4}{5} + \frac{- 16}{5 \cdot 25} \cdot 5 \cdot \frac{3}{7}$

Step 1.17.3

Rewrite the expression.

$- \frac{4}{5} + \frac{- 16}{25} \cdot \frac{3}{7}$

Step 1.18

Move the negative in front of the fraction.

$- \frac{4}{5} - \frac{16}{25} \cdot \frac{3}{7}$

Step 1.19

Multiply $- \frac{16}{25} \cdot \frac{3}{7}$ .

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Step 1.19.1

Multiply $\frac{3}{7}$ by $\frac{16}{25}$ .

$- \frac{4}{5} - \frac{3 \cdot 16}{7 \cdot 25}$

Step 1.19.2

Multiply $3$ by $16$ .

$- \frac{4}{5} - \frac{48}{7 \cdot 25}$

Step 1.19.3

Multiply $7$ by $25$ .

$- \frac{4}{5} - \frac{48}{175}$

Step 2

To write $- \frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{35}{35}$ .

$- \frac{4}{5} \cdot \frac{35}{35} - \frac{48}{175}$

Step 3

Write each expression with a common denominator of $175$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{4}{5}$ by $\frac{35}{35}$ .

$- \frac{4 \cdot 35}{5 \cdot 35} - \frac{48}{175}$

Step 3.2

Multiply $5$ by $35$ .

$- \frac{4 \cdot 35}{175} - \frac{48}{175}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 4 \cdot 35 - 48}{175}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 4$ by $35$ .

$\frac{- 140 - 48}{175}$

Step 5.2

Subtract $48$ from $- 140$ .

$\frac{- 188}{175}$

Step 6

Move the negative in front of the fraction.

$- \frac{188}{175}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{188}{175}$

Decimal Form:

$- 1.07428571 \dots$

Mixed Number Form:

$- 1 \frac{13}{175}$