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
1/3
3
−1/3
The rational exponent that is equivalent to the expression 216√3 is 2/3.
Using the properties of exponents to generate an equivalent expression, which of the following would be the rational exponent on an expression equivalent to 3√216
?(1 point)
Responses
−3
1/3
3
−1/3
The rational exponent that is equivalent to the expression ∛216 is 1/3.
Which of the following is an equivalent expression for (5^1/2)/3√125
when simplified using exponent properties?(1 point)
Responses
√5/5
1
5^0
1/5
The equivalent expression for (5^1/2)/(3√125) when simplified using exponent properties is √5/5.
Which of the following is an equivalent expression to 81 ^ -1/2
?(1 point)
Responses
1/√81
√81
−√81
−1/√81
An equivalent expression to 81 ^ -1/2 is 1/√81.
Use the properties of exponents to determine whether the equation 10^ -1/3 = 3√10 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.
False, because according to the Negative Exponent Rule, the equation should be 10^ -1/3 = −1/ 3√10
True, because the Negative Exponent Rule requires that the number be rewritten as a negative value
False, because the Negative Exponent Rule requires that the number be rewritten as a quotient, not as a negative value.
.
.
True, because the negative sign moves to the front when writing an equivalent expression.
Use the properties of exponents to generate an equivalent expression for 3√8/√2
To generate an equivalent expression for 3√8/√2, we can simplify each term separately using the property of exponents.
First, simplify 3√8. This can be written as 8^(1/3).
Next, simplify √2. This can be written as 2^(1/2).
Now, we can rewrite the expression with the simplified terms:
(8^(1/3))/(2^(1/2))
Finally, using the property of exponents, we can simplify further by changing the division into multiplication and subtracting the exponents:
8^(1/3) * (2^(-1/2))
So, an equivalent expression is 8^(1/3) * (2^(-1/2)).
Use the Quotient Property and Negative Exponent Property to generate an equivalent expression for √49/ 7^ −3
. What will the rational exponent be for the new expression?
To generate an equivalent expression for √49/7^−3 using the Quotient Property and Negative Exponent Property, we can simplify each term separately.
First, let's simplify √49. The square root of 49 is 7.
Next, let's simplify 7^−3 using the Negative Exponent Property. When we have a negative exponent, we can rewrite the expression as the reciprocal of the base with the positive exponent. In this case, 7^−3 can be written as 1/(7^3).
Now, we can rewrite the expression with the simplified terms:
√49/7^−3 = 7/(1/(7^3)).
Using the Quotient Property, we can change the division into multiplication by taking the reciprocal of the denominator:
7/(1/(7^3)) = 7 * (7^3/1).
Simplifying further, we can multiply the 7 with the (7^3/1):
7 * (7^3/1) = 7^1 * 7^3.
Using the Product of Powers Property, we can add the exponents:
7^1 * 7^3 = 7^(1+3) = 7^4.
So, the equivalent expression for √49/7^−3 is 7^4. The rational exponent for the new expression is 4.