Solve (-7)^3+(-2)^3-[(-21)+35-sqrt[3]{125}*(-8)]

$$( - 7 ) ^ { 3 } + ( - 2 ) ^ { 3 } - [ ( - 21 ) + 35 - \sqrt[ 3 ] { 125 } \times ( - 8 ) ]$$

Evaluate

$$-405$$

Solution Steps

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

$$-343+\left(-2\right)^{3}-\left(-21+35-\sqrt[3]{125}\left(-8\right)\right)$$

Calculate -2 to the power of 3 and get -8.

$$-343-8-\left(-21+35-\sqrt[3]{125}\left(-8\right)\right)$$

Subtract 8 from -343 to get -351.

$$-351-\left(-21+35-\sqrt[3]{125}\left(-8\right)\right)$$

Add -21 and 35 to get 14.

$$-351-\left(14-\sqrt[3]{125}\left(-8\right)\right)$$

Calculate \sqrt[3]{125} and get 5.

$$-351-\left(14-5\left(-8\right)\right)$$

Multiply 5 and -8 to get -40.

$$-351-\left(14-\left(-40\right)\right)$$

The opposite of -40 is 40.

$$-351-\left(14+40\right)$$

Add 14 and 40 to get 54.

$$-351-54$$

Subtract 54 from -351 to get -405.

$$-405$$

Factor

$$-405$$