Solve {[-2^{4}+(-3)^{3}:(-3)]*(-4)^0-(-2)^7:(-2)^4}*(-5)^2

$$\{ [ - 2 ^ { 4 } + ( - 3 ) ^ { 3 } : ( - 3 ) ] \cdot ( - 4 ) ^ { 0 } - ( - 2 ) ^ { 7 } : ( - 2 ) ^ { 4 } \} \cdot ( - 5 ) ^ { 2 }$$

Evaluate

$$25$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 3 to get 2.

$$\left(\left(-2^{4}+\left(-3\right)^{2}\right)\left(-4\right)^{0}-\frac{\left(-2\right)^{7}}{\left(-2\right)^{4}}\right)\left(-5\right)^{2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 7 to get 3.

$$\left(\left(-2^{4}+\left(-3\right)^{2}\right)\left(-4\right)^{0}-\left(-2\right)^{3}\right)\left(-5\right)^{2}$$

Calculate 2 to the power of 4 and get 16.

$$\left(\left(-16+\left(-3\right)^{2}\right)\left(-4\right)^{0}-\left(-2\right)^{3}\right)\left(-5\right)^{2}$$

Calculate -3 to the power of 2 and get 9.

$$\left(\left(-16+9\right)\left(-4\right)^{0}-\left(-2\right)^{3}\right)\left(-5\right)^{2}$$

Add -16 and 9 to get -7.

$$\left(-7\left(-4\right)^{0}-\left(-2\right)^{3}\right)\left(-5\right)^{2}$$

Calculate -4 to the power of 0 and get 1.

$$\left(-7-\left(-2\right)^{3}\right)\left(-5\right)^{2}$$

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

$$\left(-7-\left(-8\right)\right)\left(-5\right)^{2}$$

The opposite of -8 is 8.

$$\left(-7+8\right)\left(-5\right)^{2}$$

Add -7 and 8 to get 1.

$$1\left(-5\right)^{2}$$

Calculate -5 to the power of 2 and get 25.

$$1\times 25$$

Multiply 1 and 25 to get 25.

$$25$$

Factor

$$5^{2}$$