Apply the quotient role of integer exponents to simplify 23 to the exponent of 65÷23 to the exponent of 32
To simplify the expression 23^(65 ÷ 23)^32, you can first simplify the exponent 65 ÷ 23.
65 ÷ 23 = 2 remainder 19
So, 65 ÷ 23 is equal to 2 with a remainder of 19.
Now, we have:
23^(2 remainder 19)^32
According to the quotient rule of exponents, we can rewrite this as:
23^(2 × 32 + 19)
Simplifying further:
23^(64 + 19)
Now, we can calculate the value of this expression:
23^83