Respuesta :

carlosego

Answer:

[tex]10 ^ {3m-2n} = 10 ^ z[/tex]

Where z = 3m-2n

Step-by-step explanation:

An important mathematical property about the powers is that when powers of equal base are divided, the same base is placed and the exponents are subtracted.

Then we can write 1000m and 100n as powers of the same base:

[tex]1000 ^ m = (10 ^ 3) ^ m = 10 ^ {3m}\\ 100 ^ n = (10 ^ 2) ^ n = 10 ^ {2n}[/tex]

Now we perform the division of powers of the same base (10)

[tex]\frac{10 ^ {3m}}{10 ^ {2n}} = 10 ^ {3m-2n}[/tex]

Finally

 [tex]10 ^ {3m-2n} = 10 ^ z[/tex]

Where z = 3m-2n

MrRoyal

The division of the numbers are illustrations of equivalent expression.

The expression of z in terms of m and n is: [tex]\mathbf{z = \frac{m}{n} }[/tex]

From the question, we have the following highlights

  • 1000m divides 100n
  • The result is 10z

So, the expression can be represented as:

[tex]\mathbf{\frac{1000m}{100n} = 10z}[/tex]

Divide 1000 by 100

[tex]\mathbf{\frac{10m}{n} = 10z}[/tex]

Divide both sides by 10

[tex]\mathbf{\frac{10m}{10n} = z}[/tex]

Rewrite as:

[tex]\mathbf{z = \frac{10m}{10n} }[/tex]

[tex]\mathbf{z = \frac{m}{n} }[/tex]

Hence, the expression of z in terms of m and n is: [tex]\mathbf{z = \frac{m}{n} }[/tex]

Read more about equivalent expressions at:

https://brainly.com/question/15715866