Question

using the properties of exponents to generate an equivalent expression which of the following would be rational exponent on an equivalent to 3/216

Answer 1

using the properties of exponents to generate anV equivalent expression which of the following would be rational exponent on an equivalent to 3 and the sqare root of 216

Answer 2

To find an equivalent expression with rational exponents for 3/216, we can rewrite 216 as a power of 3.

216 = 6^3

Now, we can rewrite the expression as:

(3/216) = (3/(6^3))

Finally, we can rewrite the exponent 3 as a rational exponent with a denominator of 2:

(3/(6^3)) = 3/(6^(3/2))

Therefore, a rational exponent equivalent to 3/216 is 3/(6^(3/2)).

Answer 3

To find an equivalent expression for the square root of 216 or √216, we can rewrite it as a power of 216.

216 can be expressed as 6^3. Therefore, we can rewrite the expression as:

√216 = √(6^3)

Now, we can use the property of exponents that states √(a^b) = a^(b/2):

√(6^3) = (6^3)^(1/2)

Now, we have an equivalent expression for the square root of 216 as (6^3)^(1/2).

Therefore, a rational exponent equivalent to √216 is (6^3)^(1/2).