What is [(-3^4+2^4)^2+1]\div (-13) ?

The solution to [(-3^4+2^4)^2+1]\div (-13) is -325 1/13

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Popular >

[(-3^4+2^4)^2+1]\div (-13)

Solution

[(- 3^{4} + 2^{4})^{2} + 1] \div (- 13)

Solution

- 325 \frac{1}{13}

Solution steps

[(- 3^{4} + 2^{4})^{2} + 1] \div (- 13)

Follow the PEMDAS order of operations

Calculate within parentheses

[(- 3^{4} + 2^{4})^{2} + 1] : 4226

(- 3^{4} + 2^{4})^{2} + 1

Calculate within parentheses

(- 3^{4} + 2^{4}) : - 65

- 3^{4} + 2^{4}

Calculate exponents

3^{4} : 81

3^{4}

3^{4} = 81

= 81

= - 81 + 2^{4}

Calculate exponents

2^{4} : 16

2^{4}

2^{4} = 16

= 16

= - 81 + 16

Add and subtract (left to right)

- 81 + 16 : - 65

- 81 + 16

- 81 + 16 = - 65

= - 65

= - 65

= (- 65)^{2} + 1

Calculate exponents

(- 65)^{2} : 4225

(- 65)^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 65)^{2} = 6 5^{2} = 4225

= 4225

= 4225 + 1

Add and subtract (left to right)

4225 + 1 : 4226

4225 + 1

4225 + 1 = 4226

= 4226

= 4226

= 4226 \div (- 13)

Multiply and divide (left to right)

4226 \div (- 13) : \frac{4226}{( - 13 )}

4226 \div (- 13)

Apply rule

a \div (- b) = - a \div b

4226 \div (- 13) = - 4226 \div 13 = \frac{4226}{( - 13 )}

= \frac{4226}{( - 13 )}

= \frac{4226}{( - 13 )}

Simplify

\frac{4226}{( - 13 )} : - 325 \frac{1}{13}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{4226}{13}

Convert improper fractions to mixed numbers:

\frac{4226}{13} = 325 \frac{1}{13}

\frac{4226}{13} = 325

Remainder

1

\frac{4226}{13}

Write the problem in long division format

13 \overline{∣ 4226}

Divide

42

13

to get

3

Divide

42

13

to get

3

3 13 \overline{∣ 4226}

Multiply the quotient digit

(3)

by the divisor

13

3 13 \overline{∣ 4226} \underline{39}

Subtract

39

from

42

3 13 \overline{∣ 4226} \underline{39} 3

Bring down the next number of the dividend

3 13 \overline{∣ 4226} \underline{39} 32

3 13 \overline{∣ 4226} \underline{39} 32

Divide

32

13

to get

2

Divide

32

13

to get

2

32 13 \overline{∣ 4226} \underline{39} 32

Multiply the quotient digit

(2)

by the divisor

13

32 13 \overline{∣ 4226} \underline{39} 32 \underline{26}

Subtract

26

from

32

32 13 \overline{∣ 4226} \underline{39} 32 \underline{26} 6

Bring down the next number of the dividend

32 13 \overline{∣ 4226} \underline{39} 32 \underline{26} 66

32 13 \overline{∣ 4226} \underline{39} 32 \underline{26} 66

Divide

66

13

to get

5

Divide

66

13

to get

5

325 13 \overline{∣ 4226} \underline{39} 32 \underline{26} 66

Multiply the quotient digit

(5)

by the divisor

13

325 13 \overline{∣ 4226} \underline{39} 32 \underline{26} 66 \underline{65}

Subtract

65

from

66

325 13 \overline{∣ 4226} \underline{39} 32 \underline{26} 66 \underline{65} 1

325 13 \overline{∣ 4226} \underline{39} 32 \underline{26} 66 \underline{65} 1

The solution for Long Division of

\frac{4226}{13}

325

with remainder of

1

325 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{4226}{13} = 325 \frac{1}{13}

= 325 \frac{1}{13}

= - 325 \frac{1}{13}

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\frac{2 + 0 - 7 - 7 - 5 - 7 - 5 + 1 + 2 - 5}{10}

8+(-25)+16(-25)-16

8 + (- 25) + 16 (- 25) - 16

Frequently Asked Questions (FAQ)

What is [(-3^4+2^4)^2+1]\div (-13) ?
The solution to [(-3^4+2^4)^2+1]\div (-13) is -325 1/13