What is the exponent in an equivalent form to the expression 1 to the 1st power ⋅ 1 to the 3rd power if the base is 1?
Any number (except 0) raised to the power of 0 is equal to 1. Therefore, in this case, the exponent is 0.
If the base is 1, any number raised to any power will still be 1. Therefore, in an equivalent form, the exponent doesn't matter.
To find the exponent in an equivalent form to the expression 1 to the 1st power ⋅ 1 to the 3rd power if the base is 1, we need to understand the properties of exponents and the rules for multiplying powers with the same base.
In this expression, we have the base of 1 and two exponents, 1 and 3.
When we have the same base raised to different exponents and we want to multiply them together, we can keep the base the same and add the exponents. So, 1 to the 1st power ⋅ 1 to the 3rd power is equal to 1^(1+3), which simplifies to 1^4.
Using the exponent rule that any number raised to the power of 1 is itself, we know that 1^4 is equal to 1.
Therefore, the equivalent form of the expression 1 to the 1st power ⋅ 1 to the 3rd power, with the base of 1, is 1^4 or simply 1.