Solve [(+30):(-6)+1]^{2}-[(-3)^{4}]^{3}:[(-3)^{3}(-3)^9]-{[(-10)^2]^0}^0

$$[ ( + 30 ) : ( - 6 ) + 1 ] ^ { 2 } - [ ( - 3 ) ^ { 4 } ] ^ { 3 } : [ ( - 3 ) ^ { 3 } ( - 3 ) ^ { 9 } ] - \{ [ ( - 10 ) ^ { 2 } ] ^ { 0 } \} ^ { 0 }$$

Evaluate

$$14$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\left(\frac{30}{-6}+1\right)^{2}-\frac{\left(-3\right)^{12}}{\left(-3\right)^{3}\left(-3\right)^{9}}-\left(\left(\left(-10\right)^{2}\right)^{0}\right)^{0}$$

To multiply powers of the same base, add their exponents. Add 3 and 9 to get 12.

$$\left(\frac{30}{-6}+1\right)^{2}-\frac{\left(-3\right)^{12}}{\left(-3\right)^{12}}-\left(\left(\left(-10\right)^{2}\right)^{0}\right)^{0}$$

Divide \left(-3\right)^{12} by \left(-3\right)^{12} to get 1.

$$\left(\frac{30}{-6}+1\right)^{2}-1-\left(\left(\left(-10\right)^{2}\right)^{0}\right)^{0}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 0 to get 0.

$$\left(\frac{30}{-6}+1\right)^{2}-1-\left(\left(-10\right)^{0}\right)^{0}$$

To raise a power to another power, multiply the exponents. Multiply 0 and 0 to get 0.

$$\left(\frac{30}{-6}+1\right)^{2}-1-\left(-10\right)^{0}$$

Divide 30 by -6 to get -5.

$$\left(-5+1\right)^{2}-1-\left(-10\right)^{0}$$

Add -5 and 1 to get -4.

$$\left(-4\right)^{2}-1-\left(-10\right)^{0}$$

Calculate -4 to the power of 2 and get 16.

$$16-1-\left(-10\right)^{0}$$

Subtract 1 from 16 to get 15.

$$15-\left(-10\right)^{0}$$

Calculate -10 to the power of 0 and get 1.

$$15-1$$

Subtract 1 from 15 to get 14.

$$14$$

Factor

$$2\times 7$$