Question
Select the correct answer to the following equation: x54=243
.(1 point)
Responses
3
3
27
27
no solution
no solution
81
.(1 point)
Responses
3
3
27
27
no solution
no solution
81
Answers
Answer
the 5 and 4 is a fraction
Answer
Use the properties of exponents and radicals to generate an equivalent expression for (256√10)551213
.(1 point)
.(1 point)
Answer
Is the equation 5−5⋅(5–√3)12=15
true or false? Enter 1 for true or 2 for false.(1 point)
true or false? Enter 1 for true or 2 for false.(1 point)
Answer
Use the Commutative Property of Multiplication to rewrite the algebraic expression: j37⋅h24
.(1 point)
.(1 point)
Answer
Question
Use the Distributive Property to rewrite the expression (2x−2)(x−6)
.(1 point)
Responses
3x2−10x−8
3 x squared minus 10 x minus 8
2x2+10x−10
2 x squared plus 10 x minus 10
x2−8x+12
x squared minus 8 x plus 12
2x2−14x+12
Use the Distributive Property to rewrite the expression (2x−2)(x−6)
.(1 point)
Responses
3x2−10x−8
3 x squared minus 10 x minus 8
2x2+10x−10
2 x squared plus 10 x minus 10
x2−8x+12
x squared minus 8 x plus 12
2x2−14x+12
Answered by
GPT-4o mini
To solve the equation \( x^5 = 243 \), we need to determine what \( x \) equals.
First, we can express 243 as a power of 3:
\[
243 = 3^5
\]
Now we can substitute this back into the equation:
\[
x^5 = 3^5
\]
To solve for \( x \), we can take the fifth root of both sides:
\[
x = 3
\]
So the correct answer is:
**3**
First, we can express 243 as a power of 3:
\[
243 = 3^5
\]
Now we can substitute this back into the equation:
\[
x^5 = 3^5
\]
To solve for \( x \), we can take the fifth root of both sides:
\[
x = 3
\]
So the correct answer is:
**3**
Answered by
GPT-4o mini
Thank you for your clarification! If the equation is written as \( x^{\frac{5}{4}} = 243 \), we can solve it as follows:
1. Rewrite the equation:
\[
x^{\frac{5}{4}} = 243
\]
2. Raise both sides to the power of \(\frac{4}{5}\) to solve for \(x\):
\[
x = 243^{\frac{4}{5}}
\]
3. Calculate \(243^{\frac{1}{5}}\):
\[
243 = 3^5 \implies 243^{\frac{1}{5}} = 3
\]
4. Now calculate:
\[
x = 3^4 = 81
\]
Therefore, the correct answer is:
**81**
1. Rewrite the equation:
\[
x^{\frac{5}{4}} = 243
\]
2. Raise both sides to the power of \(\frac{4}{5}\) to solve for \(x\):
\[
x = 243^{\frac{4}{5}}
\]
3. Calculate \(243^{\frac{1}{5}}\):
\[
243 = 3^5 \implies 243^{\frac{1}{5}} = 3
\]
4. Now calculate:
\[
x = 3^4 = 81
\]
Therefore, the correct answer is:
**81**
Answered by
GPT-4o mini
To simplify the expression \((256\sqrt{10})^{551213}\), we can use the properties of exponents.
1. **Separate the base using the power of a product property**:
\[
(256 \sqrt{10})^{551213} = 256^{551213} \cdot (\sqrt{10})^{551213}
\]
2. **Rewrite \(\sqrt{10}\) in exponent form**:
\[
\sqrt{10} = 10^{1/2}
\]
Thus, we have:
\[
(\sqrt{10})^{551213} = (10^{1/2})^{551213} = 10^{\frac{551213}{2}}
\]
3. **Now simplify \(256^{551213}\)**:
Since \(256 = 2^8\), we can write:
\[
256^{551213} = (2^8)^{551213} = 2^{8 \cdot 551213} = 2^{4409704}
\]
4. **Combine the two parts**:
Substituting back, we get:
\[
(256\sqrt{10})^{551213} = 2^{4409704} \cdot 10^{\frac{551213}{2}}
\]
Thus, the final equivalent expression for \((256\sqrt{10})^{551213}\) is:
\[
2^{4409704} \cdot 10^{\frac{551213}{2}}
\]
1. **Separate the base using the power of a product property**:
\[
(256 \sqrt{10})^{551213} = 256^{551213} \cdot (\sqrt{10})^{551213}
\]
2. **Rewrite \(\sqrt{10}\) in exponent form**:
\[
\sqrt{10} = 10^{1/2}
\]
Thus, we have:
\[
(\sqrt{10})^{551213} = (10^{1/2})^{551213} = 10^{\frac{551213}{2}}
\]
3. **Now simplify \(256^{551213}\)**:
Since \(256 = 2^8\), we can write:
\[
256^{551213} = (2^8)^{551213} = 2^{8 \cdot 551213} = 2^{4409704}
\]
4. **Combine the two parts**:
Substituting back, we get:
\[
(256\sqrt{10})^{551213} = 2^{4409704} \cdot 10^{\frac{551213}{2}}
\]
Thus, the final equivalent expression for \((256\sqrt{10})^{551213}\) is:
\[
2^{4409704} \cdot 10^{\frac{551213}{2}}
\]
Answered by
GPT-4o mini
Let's evaluate the equation \( 5 - 5 \cdot (5 - \sqrt{3})^{12} = 15 \).
1. **First, isolate the term involving the exponent**:
\[
5 - 5 \cdot (5 - \sqrt{3})^{12} = 15
\]
Rearranging gives:
\[
-5 \cdot (5 - \sqrt{3})^{12} = 15 - 5
\]
\[
-5 \cdot (5 - \sqrt{3})^{12} = 10
\]
2. **Divide both sides by -5**:
\[
(5 - \sqrt{3})^{12} = -2
\]
The left side, \((5 - \sqrt{3})^{12}\), is a positive number because \(5 - \sqrt{3} > 0\) and any positive number raised to a power is also positive.
The right side is \(-2\), which is negative.
Since a positive number cannot equal a negative number, the statement is **false**.
Thus, the answer is:
**2** (false).
1. **First, isolate the term involving the exponent**:
\[
5 - 5 \cdot (5 - \sqrt{3})^{12} = 15
\]
Rearranging gives:
\[
-5 \cdot (5 - \sqrt{3})^{12} = 15 - 5
\]
\[
-5 \cdot (5 - \sqrt{3})^{12} = 10
\]
2. **Divide both sides by -5**:
\[
(5 - \sqrt{3})^{12} = -2
\]
The left side, \((5 - \sqrt{3})^{12}\), is a positive number because \(5 - \sqrt{3} > 0\) and any positive number raised to a power is also positive.
The right side is \(-2\), which is negative.
Since a positive number cannot equal a negative number, the statement is **false**.
Thus, the answer is:
**2** (false).
Answered by
GPT-4o mini
The Commutative Property of Multiplication states that the order of factors can be changed without affecting the product. Therefore, the expression \( j^{37} \cdot h^{24} \) can be rewritten by swapping the two factors.
So, using the Commutative Property, the expression can be rewritten as:
\[
h^{24} \cdot j^{37}
\]
This is the equivalent expression using the Commutative Property of Multiplication.
So, using the Commutative Property, the expression can be rewritten as:
\[
h^{24} \cdot j^{37}
\]
This is the equivalent expression using the Commutative Property of Multiplication.
Answered by
GPT-4o mini
To use the Distributive Property to rewrite the expression \((2x - 2)(x - 6)\), we will distribute each term in the first parenthesis to each term in the second parenthesis.
Using the distributive property, we have:
\[
(2x - 2)(x - 6) = 2x \cdot x + 2x \cdot (-6) - 2 \cdot x - 2 \cdot (-6)
\]
Now calculating each part:
1. \(2x \cdot x = 2x^2\)
2. \(2x \cdot (-6) = -12x\)
3. \(-2 \cdot x = -2x\)
4. \(-2 \cdot (-6) = +12\)
Now combine them all together:
\[
2x^2 - 12x - 2x + 12
\]
Combine the like terms \(-12x\) and \(-2x\):
\[
2x^2 - 14x + 12
\]
Thus, the rewritten expression using the Distributive Property is:
**2x^2 - 14x + 12**
Using the distributive property, we have:
\[
(2x - 2)(x - 6) = 2x \cdot x + 2x \cdot (-6) - 2 \cdot x - 2 \cdot (-6)
\]
Now calculating each part:
1. \(2x \cdot x = 2x^2\)
2. \(2x \cdot (-6) = -12x\)
3. \(-2 \cdot x = -2x\)
4. \(-2 \cdot (-6) = +12\)
Now combine them all together:
\[
2x^2 - 12x - 2x + 12
\]
Combine the like terms \(-12x\) and \(-2x\):
\[
2x^2 - 14x + 12
\]
Thus, the rewritten expression using the Distributive Property is:
**2x^2 - 14x + 12**
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.