Using the properties of exponents to generate an equivalent expression, which of the following would be the rational exponent on an expression equivalent to 216−−−√3? show your work.(1 point)
Responses
−3
negative 3
3
3
13
Start Fraction 1 over 3 End Fraction
−13
Start Fraction 1 over 3 End Fraction
To generate an equivalent expression for √216 using rational exponents, we can first rewrite 216 as a power of 6.
216 can be written as 6^3, because 6 * 6 * 6 = 216.
Now, we can rewrite the expression as (6^3)^(1/3).
When we raise a power to another power, we multiply the exponents. So, (6^3)^(1/3) becomes 6^(3 * 1/3).
3 * 1/3 is equal to 1. So, the expression becomes 6^1.
Therefore, the equivalent expression for √216 using rational exponents is 6^1.
3 is the rational exponent on this expression.