Solve [(-4:2^{2}-9:3^{2}-1^3)*(-3^5:3^3+1)]:(-5^2+1)

$$[ ( - 4 : 2 ^ { 2 } - 9 : 3 ^ { 2 } - 1 ^ { 3 } ) \cdot ( - 3 ^ { 5 } : 3 ^ { 3 } + 1 ) ] : ( - 5 ^ { 2 } + 1 )$$

Evaluate

$$-1$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{\left(\frac{-4}{4}-\frac{9}{3^{2}}-1^{3}\right)\left(\frac{-3^{5}}{3^{3}}+1\right)}{-5^{2}+1}$$

Divide -4 by 4 to get -1.

$$\frac{\left(-1-\frac{9}{3^{2}}-1^{3}\right)\left(\frac{-3^{5}}{3^{3}}+1\right)}{-5^{2}+1}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\left(-1-\frac{9}{9}-1^{3}\right)\left(\frac{-3^{5}}{3^{3}}+1\right)}{-5^{2}+1}$$

Divide 9 by 9 to get 1.

$$\frac{\left(-1-1-1^{3}\right)\left(\frac{-3^{5}}{3^{3}}+1\right)}{-5^{2}+1}$$

Subtract 1 from -1 to get -2.

$$\frac{\left(-2-1^{3}\right)\left(\frac{-3^{5}}{3^{3}}+1\right)}{-5^{2}+1}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{\left(-2-1\right)\left(\frac{-3^{5}}{3^{3}}+1\right)}{-5^{2}+1}$$

Subtract 1 from -2 to get -3.

$$\frac{-3\left(\frac{-3^{5}}{3^{3}}+1\right)}{-5^{2}+1}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{-3\left(\frac{-243}{3^{3}}+1\right)}{-5^{2}+1}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{-3\left(\frac{-243}{27}+1\right)}{-5^{2}+1}$$

Divide -243 by 27 to get -9.

$$\frac{-3\left(-9+1\right)}{-5^{2}+1}$$

Add -9 and 1 to get -8.

$$\frac{-3\left(-8\right)}{-5^{2}+1}$$

Multiply -3 and -8 to get 24.

$$\frac{24}{-5^{2}+1}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{24}{-25+1}$$

Add -25 and 1 to get -24.

$$\frac{24}{-24}$$

Divide 24 by -24 to get -1.

$$-1$$

Factor

$$-1$$