Question

1000 to the power of m divided by 100 to the power of n =10 to the power of z

express z in terms of m and n

Answer 1

Answer:

Step-by-step explanation:

Consider 1000 and 100 as their respective powers of 10.

1000=10^3 and 100 = 10^2

Now recall exponent rules. An exponential expression raised to an exponent multiplies those exponents so

1000^m = (10^3)^m = 10^(3m)

And

100^n = (10^2)^n = 10^(2n)

Finally, we want to divide 10^(3m) by 10^(2n). This is another case of exponent rules. If you divide two exponential expressions with the same base, you subtract the exponents. Therefore:

(10^(3m))/(10^(2n)) = 10^(3m-2n)

And z = 3m-2n

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