Question

1000m divided by 100n can be written in the form 10z. Express z in terms of m and n

Answer 1

Answer:

$10 ^ {3m-2n} = 10 ^ z$

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:

$1000 ^ m = (10 ^ 3) ^ m = 10 ^ {3m}\\ 100 ^ n = (10 ^ 2) ^ n = 10 ^ {2n}$

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

$\frac{10 ^ {3m}}{10 ^ {2n}} = 10 ^ {3m-2n}$

Finally

 $10 ^ {3m-2n} = 10 ^ z$

Where z = 3m-2n

Answer 2

Answer:

the answer is z = 3m-2n

step by step explanation: