Use the Power Rule of Exponents to create an expression equivalent to (156)2.(1 point)
Responses
1512
15 superscript 12 baseline
154
15 superscript 4 baseline
153
15 cubed
158
Using the Power Rule of Exponents, we can simplify (15^6)^2 as 15^(6 * 2) = 15^12.
Therefore, the correct option is 15^12.
To find the exponent that would make the two expressions equivalent, we can equate the exponents in both expressions.
The given equation is: (3^3)^x = 3^24
Using the Power Rule of Exponents, we can simplify the left side of the equation as 3^(3 * x) = 3^24.
To make the two expressions equivalent, we can equate the exponents:
3 * x = 24
Dividing both sides by 3, we get:
x = 8
Therefore, the correct option is 8.
None of the given options are equivalent to (156)^2.
Using the Power Rule of Exponents, we can simplify (156)^2 as 15^2 * 6^2 = 225 * 36 = 8100.
Therefore, none of the given options are correct.
Use the Power Rule of Exponents to create an expression equivalent to (15^6)^2.(1 point)
Responses
1512
15 superscript 12 baseline
154
15 superscript 4 baseline
153
15 cubed
158
What exponent would make the two expressions equivalent: (3^3)^x=3^24?(1 point)
Responses
21
21
8
8
15
15
27
Apply the Property of Negative Integer Exponents to rewrite 15^−38 as an expression with positive exponents only.(1 point)
15^−38=
To rewrite 15^−38 as an expression with positive exponents, we can use the property of negative integer exponents, which states that a negative exponent is equal to its reciprocal with a positive exponent.
So, 15^−38 can be rewritten as 1/(15^38).
Therefore, 15^−38 = 1/(15^38).
Apply the Property of Negative Integer Exponents to rewrite 9^−23 as an expression with positive exponents only.(1 point)
9^−23=
To rewrite 9^−23 as an expression with positive exponents, we can use the property of negative integer exponents, which states that a negative exponent is equal to its reciprocal with a positive exponent.
So, 9^−23 can be rewritten as 1/(9^23).
Therefore, 9^−23 = 1/(9^23).
Apply the Property of Negative Integer Exponents to solve 3^−4. The answer should not contain any exponent expression or decimals.(1 point)
3^−4=
To solve 3^−4 using the property of negative integer exponents, we can rewrite it as the reciprocal with a positive exponent:
3^−4 = 1/(3^4)
Simplifying further:
3^−4 = 1/81
Therefore, 3^−4 = 1/81.
Question
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7^−3⋅7^−5 with positive exponents only.(1 point)
7^−3⋅7^−5=
To generate an expression equivalent to 7^−3⋅7^−5 with positive exponents only, we can use the property of negative integer exponents which states that when multiplying with the same base, you can add the exponents.
So, 7^−3⋅7^−5 can be rewritten as 7^(−3 + −5).
Simplifying further:
7^(−3 + −5) = 7^−8.
To convert this to positive exponents, we can rewrite it as the reciprocal with a positive exponent:
7^−8 = 1/(7^8).
Therefore, 7^−3⋅7^−5 can be expressed as 1/(7^8).
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5^−9/4^−12 with positive exponents only.(1 point)
5^−9/4^−12=
To generate an expression equivalent to 5^−9/4^−12 with positive exponents only, we can use the property of negative integer exponents which states that when dividing with the same base, you can subtract the exponents.
So, 5^−9/4^−12 can be rewritten as 5^(−9) / 4^(−12).
To convert the negative exponents to positive exponents, we can rewrite them as their reciprocals with positive exponents:
5^(−9) = 1/5^9 and 4^(−12) = 1/4^12.
Substituting these values into the expression:
5^−9/4^−12 = (1/5^9) / (1/4^12).
To divide fractions, we can multiply the numerator by the reciprocal of the denominator:
(1/5^9) / (1/4^12) = (1/5^9) * (4^12/1).
Simplifying further:
(1/5^9) * (4^12/1) = (4^12) / (5^9).
Therefore, 5^−9/4^−12 can be expressed as (4^12) / (5^9).