Simplify this expression using the Quotient Rule of Integer Exponents: 1253÷753 .(1 point)
Responses
5106
5 superscript 106 baseline
12106
12 superscript 106 baseline
553
5 superscript 53 baseline
1253÷753
12 superscript 53 baseline divided by 7 superscript 53 baseline
The Quotient Rule of Integer Exponents states that for any non-zero integer 'a' and integers 'm' and 'n', the following is true:
a^m ÷ a^n = a^(m-n)
Applying this rule to the expression provided,
1253 ÷ 753 means taking the number 5 raised to the power of 253 divided by the number 5 raised to the power of 53.
Using the rule we get:
5^(253) ÷ 5^(53) = 5^(253-53) = 5^(200)
So the simplified form of the expression is:
5^200
Among the options provided, the correct simplification using the Quotient Rule of Integer Exponents is:
5^200
None of the multiple choice options exactly matches this, but it seems likely that "5106" is a typographical error for "5200". If that's the case, then the correct response from the options provided would be "5106" under the assumption it's meant to represent 5^200. However, if the options are taken literally, then none of them are correct.