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)).
just show me the answer
The equivalent expression for 5 1/2 /125√3 when simplified using exponent properties is: 5/ (250 * 3^(1/4)).
Which of the following is an equivalent expression to 81−1/2?(1 point)
Responses
1/81√
Start Fraction 1 over Start Root 81 End Root End Fraction
−81−−√
negative Start Root 81 End Root
−1/81√
negative Start Fraction 1 over Start Root 81 End Root End Fraction
81−−√
The correct answer is 1/81√ or Start Fraction 1 over Start Root 81 End Root. An equivalent expression for 81^(-1/2) can be written as the reciprocal of the square root of 81.
Use the properties of exponents to determine whether the equation 10−13=−10−−√3 is true or false. Select the response that correctly answers the question and provides the appropriate justification.(1 point)
Responses
True, because the negative sign moves to the front when writing an equivalent expression.
True, because the negative sign moves to the front when writing an equivalent expression.
False, because the Negative Exponent Rule requires that the number be rewritten as a quotient, not as a negative value.
False, because the Negative Exponent Rule requires that the number be rewritten as a quotient, not as a negative value.
False, because according to the Negative Exponent Rule, the equation should be 10−13=−110√3.
False, because according to the Negative Exponent Rule, the equation should be 10 superscript negative Start Fraction 1 over 3 End Fraction baseline equals negative Start Fraction 1 over root index 3 Start Root 10 End Root End Fraction .
True, because the Negative Exponent Rule requires that the number be rewritten as a negative value
The correct answer is False, because according to the Negative Exponent Rule, the equation should be 10^(-13) = -1/(10^(1/3)). The Negative Exponent Rule requires representing a negative exponent as a reciprocal, not as a negative value.
Is the equation 3^−5⋅(81√4)^3 / 3^−4 = 3−6 true or false? Select the response that correctly answers the question and provides the appropriate justification.(1 point)
Responses
True, but the equation should be simplified using the Negative Exponent Rule.
True, but the equation should be simplified using the Negative Exponent Rule.
True. All rules have been applied correctly.
True. All rules have been applied correctly.
False. There is an error in applying the Product Property.
False. There is an error in applying the Product Property.
False. There is an error in calculation using the Quotient Property.
False. There is an error in calculation using the Quotient Property.
The correct answer is True, but the equation should be simplified using the Negative Exponent Rule.
To simplify the equation, we apply the Negative Exponent Rule which states that a^(-n) = 1/(a^n).
Using this rule, we can rewrite 3^(-5) as 1/3^5 and 3^(-4) as 1/3^4.
The equation becomes (1/3^5 * (81√4)^3) / (1/3^4) = 3^(-6).
Simplifying further, we can rewrite (81√4)^3 as 81^3 * 4^(3/2).
Substituting these values into the equation, we get (1/3^5 * 81^3 * 4^(3/2)) / (1/3^4) = 3^(-6).
Simplifying each side, we have (1/3^5 * 81^3 * 4^(3/2)) / (1/3^4) = 81^3 * 4^(3/2) = 3^(-6).
Both sides of the equation are equivalent and simplified, so the equation is true.
hey anonomis how many of these were correct for us man?
nvm I failed
answers are as follows
c
c
a
b
a