Simplify (56÷((7-9)^3)-25)/(23-5*4)

$\frac{56 \div {(7 - 9)}^{3} - 25}{23 - 5 \cdot 4}$

Step 1

Multiply the numerator and denominator of the complex fraction by ${(7 - 9)}^{3}$ .

Multiply $\frac{56 \div {(7 - 9)}^{3} - 25}{23 - 5 \cdot 4}$ by $\frac{{(7 - 9)}^{3}}{{(7 - 9)}^{3}}$ .

$\frac{{(7 - 9)}^{3}}{{(7 - 9)}^{3}} \cdot \frac{56 \div {(7 - 9)}^{3} - 25}{23 - 5 \cdot 4}$

Combine.

$\frac{{(7 - 9)}^{3} (56 \div {(7 - 9)}^{3} - 25)}{{(7 - 9)}^{3} (23 - 5 \cdot 4)}$

Step 2

Apply the distributive property.

$\frac{{(7 - 9)}^{3} 56 \div {(7 - 9)}^{3} + {(7 - 9)}^{3} \cdot - 25}{{(7 - 9)}^{3} \cdot 23 + {(7 - 9)}^{3} (- 5 \cdot 4)}$

Step 3

Simplify the denominator.

Subtract $9$ from $7$ .

$\frac{{(7 - 9)}^{3} 56 \div {(- 2)}^{3} + {(7 - 9)}^{3} \cdot - 25}{{(7 - 9)}^{3} \cdot 23 + {(7 - 9)}^{3} (- 5 \cdot 4)}$

Raise $- 2$ to the power of $3$ .

$\frac{{(7 - 9)}^{3} 56 \div (- 8) + {(7 - 9)}^{3} \cdot - 25}{{(7 - 9)}^{3} \cdot 23 + {(7 - 9)}^{3} (- 5 \cdot 4)}$

Step 4

Simplify the numerator.

Subtract $9$ from $7$ .

$\frac{{(- 2)}^{3} 56 \div (- 8) + {(7 - 9)}^{3} \cdot - 25}{{(7 - 9)}^{3} \cdot 23 + {(7 - 9)}^{3} (- 5 \cdot 4)}$

Raise $- 2$ to the power of $3$ .

$\frac{- 8 (56 \div (- 8)) + {(7 - 9)}^{3} \cdot - 25}{{(7 - 9)}^{3} \cdot 23 + {(7 - 9)}^{3} (- 5 \cdot 4)}$

Divide $56$ by $- 8$ .

$\frac{- 8 \cdot - 7 + {(7 - 9)}^{3} \cdot - 25}{{(7 - 9)}^{3} \cdot 23 + {(7 - 9)}^{3} (- 5 \cdot 4)}$

Multiply $- 8$ by $- 7$ .

$\frac{56 + {(7 - 9)}^{3} \cdot - 25}{{(7 - 9)}^{3} \cdot 23 + {(7 - 9)}^{3} (- 5 \cdot 4)}$

Subtract $9$ from $7$ .

$\frac{56 + {(- 2)}^{3} \cdot - 25}{{(7 - 9)}^{3} \cdot 23 + {(7 - 9)}^{3} (- 5 \cdot 4)}$

Raise $- 2$ to the power of $3$ .

$\frac{56 - 8 \cdot - 25}{{(7 - 9)}^{3} \cdot 23 + {(7 - 9)}^{3} (- 5 \cdot 4)}$

Multiply $- 8$ by $- 25$ .

$\frac{56 + 200}{{(7 - 9)}^{3} \cdot 23 + {(7 - 9)}^{3} (- 5 \cdot 4)}$

Add $56$ and $200$ .

$\frac{256}{{(7 - 9)}^{3} \cdot 23 + {(7 - 9)}^{3} (- 5 \cdot 4)}$

Step 5

Simplify the denominator.

Subtract $9$ from $7$ .

$\frac{256}{{(- 2)}^{3} \cdot 23 + {(7 - 9)}^{3} (- 5 \cdot 4)}$

Raise $- 2$ to the power of $3$ .

$\frac{256}{- 8 \cdot 23 + {(7 - 9)}^{3} (- 5 \cdot 4)}$

Multiply $- 8$ by $23$ .

$\frac{256}{- 184 + {(7 - 9)}^{3} (- 5 \cdot 4)}$

Subtract $9$ from $7$ .

$\frac{256}{- 184 + {(- 2)}^{3} (- 5 \cdot 4)}$

Raise $- 2$ to the power of $3$ .

$\frac{256}{- 184 - 8 (- 5 \cdot 4)}$

Multiply $- 8 (- 5 \cdot 4)$ .

Multiply $- 5$ by $4$ .

$\frac{256}{- 184 - 8 \cdot - 20}$

Multiply $- 8$ by $- 20$ .

$\frac{256}{- 184 + 160}$

Add $- 184$ and $160$ .

$\frac{256}{- 24}$

Step 6

Reduce the expression by cancelling the common factors.

Cancel the common factor of $256$ and $- 24$ .

Factor $8$ out of $256$ .

$\frac{8 (32)}{- 24}$

Cancel the common factors.

Factor $8$ out of $- 24$ .

$\frac{8 \cdot 32}{8 \cdot - 3}$

Cancel the common factor.

$\frac{8 \cdot 32}{8 \cdot - 3}$

Rewrite the expression.

$\frac{32}{- 3}$

Move the negative in front of the fraction.

$- \frac{32}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{32}{3}$

Decimal Form:

$- 10.\overline{6}$

Mixed Number Form:

$- 10 \frac{2}{3}$

Simplify (56÷((7-9)^3)-25)/(23-5*4)

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