Respuesta :

Solution:

Given:

  • x = -4
  • y = 4

Substitute the values into the equation:

  • x⁶ - x/4y
  • => [(-4)⁶] - (-4)/4(4)

Simplify the numerator and the denominator:

  • => [(-4) x (-4) x (-4) x (-4) x (-4) x (-4)] + 4/16
  • => [(-64) x (-64)] + 4/16
  • => [4096] + 4/16
  • => 4100/16

Simplify the fraction:

  • => 4100/16
  • => 1025 x 4/4 x 4
  • => 1025/4

Correct option is B.

Answer:

[tex][-\frac{1023}{4} ][/tex]

Step-by-step explanation:

[tex]\frac{x^6-x}{4y}[/tex]

x = -4

y = 4

Replace all the variables with the corresponding values given:

[tex]\frac{-4^6-(-4)}{4(4)}[/tex]

Now solve,

-4 to the power of 6 is equal to -4096

[tex]\frac{-4096-(-4)}{4(4)}[/tex]

we see that we are subtracting a negative number, meaning that it'll cancel out and turn into an addition sign. Therefore:

[tex]-4096 + 4[/tex]

[tex]-4092[/tex]

[tex]\frac{-4092}{4(4)}[/tex]

4(4) is equal to 16

[tex]\frac{-4092}{16}[/tex]

When divided, you'll get a mixed fraction of [tex]-255\frac{3}{4}[/tex]

To turn into an improper fraction, simply multiply the whole number by the denominator, then add the numerator to the result.

[tex]-255 * 4 + 3[/tex]

[tex][-\frac{1023}{4} ][/tex]

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