What is \sqrt[5]{-1024(x-5)^{20}} ?

The solution to \sqrt[5]{-1024(x-5)^{20}} is -4(x-5)^4

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simplify \sqrt[5]{-1024(x-5)^{20}}

simplify

5 - 1024 (x - 5)^{20}

- 4 (x - 5)^{4}

Solution steps

5 - 1024 (x - 5)^{20}

Apply radical rule:

n ab = n a n b,

assuming

a \geq 0, b \geq 0

5 - 1024 (x - 5)^{20} = 51024 5 - (x - 5)^{20}

= 51024 5 - (x - 5)^{20}

51024 = 4

= 4 5 - (x - 5)^{20}

Apply radical rule:

n - a = - n a,

n

is odd

5 - (x - 5)^{20} = - 5 (x - 5)^{20}

= 4 (- 5 (x - 5)^{20})

Apply radical rule:

n a^{m} = a^{\frac{m}{n}},

assuming

a \geq 0

5 (x - 5)^{20} = (x - 5)^{\frac{20}{5}}

= 4 (- (x - 5)^{\frac{20}{5}})

Divide the numbers:

\frac{20}{5} = 4

= 4 (- (x - 5)^{4})

Remove parentheses:

4 (- (x - 5)^{4}) = - 4 (x - 5)^{4}

= - 4 (x - 5)^{4}

(x - 4)^{2} + 2

(x - 4)^{2} - 9

6 x + 18 y - 9 z

\frac{3 - 2 i}{1 + i}

\frac{51}{85}

What is \sqrt[5]{-1024(x-5)^{20}} ?
The solution to \sqrt[5]{-1024(x-5)^{20}} is -4(x-5)^4