simplify this expression using the quotient rule of integer exponents: 12/53 divided by 7^53

Answer 1

To simplify the expression using the quotient rule of integer exponents, we can rewrite the division as a single fraction with a negative exponent:

12/53 divided by 7^53 = 12/53 * 7^(-53)

Now, we can apply the quotient rule of integer exponents, which states that a^m / a^n = a^(m-n). In this case, we have:

12/53 * 7^(-53) = 12/53 * 7^(0-53)

Next, we simplify the expression:

7^(0-53) = 7^(-53) = 1/7^53

Now, we substitute this back into the original expression:

12/53 * 7^(-53) = 12/53 * (1/7^53)

Finally, we can simplify further by canceling out the common factor of 7 in the numerator and denominator:

(12/53) * (1/7^53) = 12/((53) * (7^53))

Therefore, the simplified expression is 12/((53) * (7^53)).