Evaluate (|((-21)^2)÷((-7)^2)+(((-21)^3)^2)÷((-21)^5)|)÷((-2)^2)

$| {(- 21)}^{2} \div {(- 7)}^{2} + {({(- 21)}^{3})}^{2} \div {(- 21)}^{5} | \div {(- 2)}^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{| {(- 21)}^{2} \div {(- 7)}^{2} + {({(- 21)}^{3})}^{2} \div {(- 21)}^{5} |}{{(- 2)}^{2}}$

Step 2

Evaluate the exponents.

Raise $- 21$ to the power of $2$ .

$\frac{| 441 \div {(- 7)}^{2} + {({(- 21)}^{3})}^{2} \div {(- 21)}^{5} |}{{(- 2)}^{2}}$

Raise $- 7$ to the power of $2$ .

$\frac{| 441 \div 49 + {({(- 21)}^{3})}^{2} \div {(- 21)}^{5} |}{{(- 2)}^{2}}$

Step 3

Simplify the numerator.

Multiply the exponents in ${({(- 21)}^{3})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{| 441 \div 49 + {(- 21)}^{3 \cdot 2} \div {(- 21)}^{5} |}{{(- 2)}^{2}}$

Multiply $3$ by $2$ .

$\frac{| 441 \div 49 + {(- 21)}^{6} \div {(- 21)}^{5} |}{{(- 2)}^{2}}$

Raise $- 21$ to the power of $6$ .

$\frac{| 441 \div 49 + 85766121 \div {(- 21)}^{5} |}{{(- 2)}^{2}}$

Step 4

Raise $- 21$ to the power of $5$ .

$\frac{| 441 \div 49 + 85766121 \div (- 4084101) |}{{(- 2)}^{2}}$

Step 5

Simplify the numerator.

To write $441 \div 49$ as a fraction with a common denominator, multiply by $\frac{83349}{83349}$ .

$\frac{| 441 \div 49 \cdot \frac{83349}{83349} + 85766121 \div (- 4084101) |}{{(- 2)}^{2}}$

To write $85766121 \div (- 4084101)$ as a fraction with a common denominator, multiply by $\frac{- 1}{- 1}$ .

$\frac{| 441 \div 49 \cdot \frac{83349}{83349} + 85766121 \div (- 4084101) \cdot \frac{- 1}{- 1} |}{{(- 2)}^{2}}$

Write each expression with a common denominator of $4084101$ , by multiplying each by an appropriate factor of $1$ .

Multiply $441 \div 49$ by $\frac{83349}{83349}$ .

$\frac{| \frac{441 \cdot 83349}{49 \cdot 83349} + 85766121 \div (- 4084101) \cdot \frac{- 1}{- 1} |}{{(- 2)}^{2}}$

Multiply $49$ by $83349$ .

$\frac{| \frac{441 \cdot 83349}{4084101} + 85766121 \div (- 4084101) \cdot \frac{- 1}{- 1} |}{{(- 2)}^{2}}$

Multiply $85766121 \div (- 4084101)$ by $\frac{- 1}{- 1}$ .

$\frac{| \frac{441 \cdot 83349}{4084101} + \frac{85766121 \cdot - 1}{- 4084101 \cdot - 1} |}{{(- 2)}^{2}}$

Multiply $- 4084101$ by $- 1$ .

$\frac{| \frac{441 \cdot 83349}{4084101} + \frac{85766121 \cdot - 1}{4084101} |}{{(- 2)}^{2}}$

Combine the numerators over the common denominator.

$\frac{| \frac{441 \cdot 83349 + 85766121 \cdot - 1}{4084101} |}{{(- 2)}^{2}}$

Simplify the numerator.

Multiply $441$ by $83349$ .

$\frac{| \frac{36756909 + 85766121 \cdot - 1}{4084101} |}{{(- 2)}^{2}}$

Multiply $85766121$ by $- 1$ .

$\frac{| \frac{36756909 - 85766121}{4084101} |}{{(- 2)}^{2}}$

Subtract $85766121$ from $36756909$ .

$\frac{| \frac{- 49009212}{4084101} |}{{(- 2)}^{2}}$

Divide $- 49009212$ by $4084101$ .

$\frac{| - 12 |}{{(- 2)}^{2}}$

The absolute value is the distance between a number and zero. The distance between $- 12$ and $0$ is $12$ .

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

Step 6

Simplify the expression.

Raise $- 2$ to the power of $2$ .

$\frac{12}{4}$

Divide $12$ by $4$ .

$3$

Evaluate (|((-21)^2)÷((-7)^2)+(((-21)^3)^2)÷((-21)^5)|)÷((-2)^2)

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