Using the properties of exponents to generate an equivalent expression, which of the following would be the rational exponent on an expression equivalent to 3√---216?(1 point)
Responses
−3
negative 3
−13
negative Start Fraction 1 over 3 End Fraction
3
3
13
13
The correct answer is -3 or negative 3. The rational exponent for a cube root is 1/3, so an expression equivalent to 3√216 can be written as 216^(1/3).
choose one
The equivalent expression for 3√216 can be written as 216^(-3).
that didn't help, choose one
Sorry for the confusion. The rational exponent on an expression equivalent to 3√216 would be -3 or negative 3.
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?(1 point)
Responses
−3
negative 3
−1/3
negative Start Fraction 1 over 3 End Fraction
3
3
13
13
The correct answer is 1/3 or positive 1/3. The rational exponent for a cube root is 1/3, so an expression equivalent to 216^(1/3) can be written as the cube root of 216.
Which of the following is an equivalent expression for 5 1/2 /125√3 when simplified using exponent properties?(1 point)
Responses
1
1
5√/5
Start Fraction Start Root 5 End Root over 5 End Fraction
1/5
Start Fraction 1 over 5 End Fraction
50
To simplify the expression 5 1/2 /125√3 using exponent properties, we can rewrite the whole number 5 as 5^1 and the mixed number 1/2 as (1/2)^1:
(5 1/2) / (125√3) = (5^1 * (1/2)^1) / (125 * 3^(1/2))
Using the property of exponents (a^m/b^m = (a/b)^m), we can simplify further:
= (5/2) / (125 * 3^(1/2))
Now, to simplify sqrt(3)^(1/2), we use the property (a^(1/n))^(m) = a^(m/n):
= (5/2) / (125 * (3^(1/2))^(1/2))
= (5/2) / (125 * 3^(1/4))
Now, we can simplify the expression further by multiplying the numerators and denominators:
= (5/2) / (125 * 3^(1/4))
= 5/ (2 * 125 * 3^(1/4))
= 5/ (250 * 3^(1/4))
Thus, the equivalent expression when simplified using exponent properties is 5/ (250 * 3^(1/4)).