Solve {(-21)^{2}:(-7)^{2}+[(-21)^3]^2:(-21)^5}:(-2)^2

$$\{ ( - 21 ) ^ { 2 } : ( - 7 ) ^ { 2 } + [ ( - 21 ) ^ { 3 } ] ^ { 2 } : ( - 21 ) ^ { 5 } \} : ( - 2 ) ^ { 2 }$$

Evaluate

$$-3$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\frac{\left(-21\right)^{2}}{\left(-7\right)^{2}}+\frac{\left(-21\right)^{6}}{\left(-21\right)^{5}}}{\left(-2\right)^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 6 to get 1.

$$\frac{\frac{\left(-21\right)^{2}}{\left(-7\right)^{2}}+\left(-21\right)^{1}}{\left(-2\right)^{2}}$$

Calculate -21 to the power of 2 and get 441.

$$\frac{\frac{441}{\left(-7\right)^{2}}+\left(-21\right)^{1}}{\left(-2\right)^{2}}$$

Calculate -7 to the power of 2 and get 49.

$$\frac{\frac{441}{49}+\left(-21\right)^{1}}{\left(-2\right)^{2}}$$

Divide 441 by 49 to get 9.

$$\frac{9+\left(-21\right)^{1}}{\left(-2\right)^{2}}$$

Calculate -21 to the power of 1 and get -21.

$$\frac{9-21}{\left(-2\right)^{2}}$$

Subtract 21 from 9 to get -12.

$$\frac{-12}{\left(-2\right)^{2}}$$

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

$$\frac{-12}{4}$$

Divide -12 by 4 to get -3.

$$-3$$

Factor

$$-3$$