Respuesta :

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The number is 5. All you have to do is make an equation based on the information you have, x will represent the missing number so, x to the power of 10 divided by x to the power of 7 is equal to 125, then solve.

Answer:

The number is 5

Step-by-step explanation:

Let the number be x

  • A number to the 10th power [tex]=[/tex] [tex]x^{10}[/tex]
  • A number to the 7th power [tex]= x^{7}[/tex]

Divided [tex]x^{10}[/tex] by [tex]x^{7}[/tex] equals to 125

[tex]\frac{x^{10} }{x^{7} } =[/tex] 125

Dividing exponential expressions

[tex]x^{10}[/tex] divided by [tex]x^{7}[/tex] [tex]=[/tex] [tex]x^{(10-7)} = x^{3}[/tex]

[tex]x^{3} =[/tex] [tex]125[/tex]

Cube root on both the side

[tex]\sqrt[3]{x^{3} } = \sqrt[3]{125}[/tex]

x [tex]=[/tex] 5