Final answer:
The expression 4⁵ is already written using a rational exponent since the exponent 5 can be considered as 5/1.
Step-by-step explanation:
To write the expression 4⁵ using rational exponents, we need to understand the concept of integer powers. Raising a number to a power, like 4³, means multiplying the number by itself a certain number of times. For example, 4³ is the same as 4 x 4 x 4. When we deal with higher powers, such as 4⁵, writing out the long multiplication would be tedious.
To express this using a rational exponent instead, we use the fact that exponents can be multiplied when raising a power to a power. For instance, (4³)4 is 4 raised to the 3rd power and then that result raised to the 4th power. This becomes 4¹² (or 4 to the 12th power) because 3 times 4 is 12. This is a general rule that applies to exponentiated quantities, as explained in mathematical texts.
Now, for expressing 4⁵ in a rational exponent format, we can view the 5 as 5/1, making it a rational number. Therefore, 4⁵ is already written with a rational exponent since any integer can be considered a fraction with a denominator of 1. Hence, the expression is already in the form required and does not need further conversion.