Question

Rewrite the expression in the form 5^n
5^10/5^12

Answer 1

To rewrite 5^10/5^12 in the form 5^n, subtract the exponents to get 5^(-2), which simplifies to 1/25.

Step-by-step explanation:

You've asked to rewrite the expression 5^10/5^12 in the form 5^n. When dividing exponential terms with the same base, you subtract the exponents. This is based on the rules of Division of Exponentials, which say:

• Divide the digit term of the numerator by the digit term of the denominator, which in this case are both 5, so they cancel out leaving us with 1.
• Subtract the exponents of the exponential terms, here it is 10 - 12.

So the operation we need to perform is:

5^10/5^12 = 5^(10-12) = 5^(-2).

The negative exponent indicates that the expression is the reciprocal of the base raised to the positive of that exponent. Hence, the simplified answer is 5^(-2), which represents 1 divided by 5 squared or 1/25.

Answer 2

Step-by-step explanation:

This problem is all about bases and exponents. Because we have a quotient and the bases are both 5's, that means that we can use the rule of exponents for quotients to rewrite and simplify:

`(5^(10))/(5^(12))=5^(10-12)=5^(-2)`

That's the simplification as long as you are "allowed" to leave the exponent as a negative number.