Solve (-7)^17:(-7)^14-7*{-7-7*[(-4)^5:(-4)^4-(-8)]}

$$( - 7 ) ^ { 17 } : ( - 7 ) ^ { 14 } - 7 \cdot \{ - 7 - 7 \cdot [ ( - 4 ) ^ { 5 } : ( - 4 ) ^ { 4 } - ( - 8 ) ] \}$$

Evaluate

$$-98$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 14 from 17 to get 3.

$$\left(-7\right)^{3}-7\left(-7-7\left(\frac{\left(-4\right)^{5}}{\left(-4\right)^{4}}-\left(-8\right)\right)\right)$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$\left(-7\right)^{3}-7\left(-7-7\left(\left(-4\right)^{1}-\left(-8\right)\right)\right)$$

Calculate -7 to the power of 3 and get -343.

$$-343-7\left(-7-7\left(\left(-4\right)^{1}-\left(-8\right)\right)\right)$$

Calculate -4 to the power of 1 and get -4.

$$-343-7\left(-7-7\left(-4-\left(-8\right)\right)\right)$$

The opposite of -8 is 8.

$$-343-7\left(-7-7\left(-4+8\right)\right)$$

Add -4 and 8 to get 4.

$$-343-7\left(-7-7\times 4\right)$$

Multiply 7 and 4 to get 28.

$$-343-7\left(-7-28\right)$$

Subtract 28 from -7 to get -35.

$$-343-7\left(-35\right)$$

Multiply 7 and -35 to get -245.

$$-343-\left(-245\right)$$

The opposite of -245 is 245.

$$-343+245$$

Add -343 and 245 to get -98.

$$-98$$

Factor

$$-98$$