Insert the corresponding expression:
Insert the corresponding expression:
\( \left(\frac{6}{8}\right)^2= \)
Insert the corresponding expression:
\( \left(\frac{3}{2}\right)^3= \)
Insert the corresponding expression:
\( \left(\frac{4}{7}\right)^2= \)
Insert the corresponding expression:
\( \left(\frac{2}{3}\right)^2= \)
Insert the corresponding expression:
\( \left(\frac{1}{3}\right)^3= \)
Insert the corresponding expression:
To solve this problem, we'll compute using the rule for powers of a fraction:
Now, let's carry out the calculations:
Step 3: .
Step 4: .
Therefore, .
We compare with the given answer choices:
Therefore, the correct answer is , which matches Choice 3.
Insert the corresponding expression:
To solve , follow these steps:
Let's evaluate:
Raise the numerator 3 to the power of 3:
Raise the denominator 2 to the power of 3:
Combine these results into the fraction .
Therefore, .
Given several answer choices, the correct choice is 4: .
Insert the corresponding expression:
To solve the problem of squaring the fraction , we will follow these steps:
The computation involves squaring both the numerator and the denominator separately. In conclusion, the squared fraction is:
Therefore, the corresponding expression for is .
Insert the corresponding expression:
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: The expression given is .
Step 2: According to the exponentiation rule, we apply the exponent to both the numerator and the denominator:
.
Step 3: Calculate and :
, and .
Step 4: Form the resultant fraction:
Thus, .
Step 5: Finally, compare this result with the given choices:
Our result matches with choice 2.
Therefore, the solution to the problem is .
Insert the corresponding expression:
To solve the expression , we need to apply the rule for exponents of a fraction, which states:
Using this property, we can rewrite the fraction with its exponent as follows:
Now, calculate the powers of the numerator and the denominator separately:
Thus, putting it all together, we have:
This shows that raising both the numerator and the denominator of a fraction to a power involves calculating the power of each part separately and then constructing a new fraction.
The solution to the question is:
Insert the corresponding expression:
\( \left(\frac{1}{2}\right)^2= \)
Insert the corresponding expression:
\( \left(\frac{4}{5}\right)^3= \)
Insert the corresponding expression:
\( \left(\frac{4}{5}\right)^2= \)
What is the result of the following power?
\( (\frac{3}{4})^2 \)
What is the result of the following power?
\( (\frac{5}{6})^2 \)
Insert the corresponding expression:
To solve this problem, we'll follow these steps:
Now, let's work through each step in detail:
Step 1: The fraction given is and the power is 2.
Step 2: Applying the formula , we have:
Step 3: Calculate .
Step 4: Calculate .
Step 5: Compile these to get .
Therefore, the solution to the problem is , which matches choice 2.
Insert the corresponding expression:
To solve this problem, we will evaluate the expression following these steps:
Let's go through each step:
Step 1: Calculate the cube of the numerator, which is 4. That is, .
Step 2: Calculate the cube of the denominator, which is 5. That is, .
Step 3: Combine these results into a fraction: .
Therefore, the expression simplifies to .
Upon comparing with the given choices, the correct answer is choice 1: .
Insert the corresponding expression:
To solve the problem of finding the value of , we will follow these steps:
Since we successfully calculated , this matches the choice labeled .
Therefore, the correct expression is .
What is the result of the following power?
To solve , you need to square both the numerator and the denominator separately:
1. Square the numerator:
2. Square the denominator:
3. Combine the results to get
What is the result of the following power?
To solve , you need to square both the numerator and the denominator separately:
1. Square the numerator:
2. Square the denominator:
3. Combine the results to get
Compute the value of:
\((\frac{3}{4})^3=\)
Evaluate the expression:
\((\frac{5}{6})^2=\)
What is the result of:
\((\frac{7}{5})^2=\)
What is the result of the following power?
\( (\frac{2}{3})^3 \)
\( (\frac{2}{6})^3= \)
Compute the value of:
To compute , you must raise both the numerator and the denominator to the power of 3:
Numerator:
Denominator:
Therefore, .
Evaluate the expression:
To evaluate , raise both the numerator and the denominator to the power of 2:
Numerator:
Denominator:
Therefore, .
What is the result of:
To determine , raise both the numerator and the denominator to the power of 2:
Numerator:
Denominator:
Therefore, .
What is the result of the following power?
To solve the given power expression, we need to apply the formula for powers of a fraction. The expression we are given is:
Let's break down the steps:
So, the result of the expression is .
We use the formula:
We simplify:
Insert the corresponding expression:
\( \left(\frac{a\times b}{2\times x}\right)^3= \)
Insert the corresponding expression:
\( \left(\frac{a\times3}{2\times x}\right)^3= \)
Insert the corresponding expression:
\( \left(\frac{6}{x\times y}\right)^2= \)
Insert the corresponding expression:
\( \left(\frac{2\times a}{3}\right)^2= \)
\( 300^{-4}\cdot(\frac{1}{300})^{-4}=? \)
Insert the corresponding expression:
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: We have the expression . According to the power of a fraction rule, , we can raise the numerator and denominator to the power of 3 separately.
Step 2: Apply the cube power:
Step 3: Combine these results:
The expression simplifies to .
Comparing it to the given choices, we find that this matches Choice 1: .
Therefore, the solution to the problem is .
Insert the corresponding expression:
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Our given expression is .
Step 2: Apply the power to the entire fraction using , we get:
.
Step 3: Simplify the numerator and the denominator separately:
Numerator: .
Denominator: .
Step 4: Combine the simplified components to form the final expression:
The expression is .
Therefore, the solution to the problem is , which corresponds to choice 2.
Insert the corresponding expression:
To solve this problem, we'll apply the rule for powers of a fraction:
Thus, the expression simplifies to .
Therefore, the correct answer is clearly the expression , which matches choice 4.
Insert the corresponding expression:
The task is to simplify .
First, applying the exponent rule for fractions, , we have:
Now, simplify each part:
Thus, the expression simplifies to .
We ensure the valid transformations based on the choices provided:
Therefore, each choice represents correct steps or forms towards the simplified expression.
The correct answer is: All answers are correct.
All answers are correct
To solve the problem , let's follow these steps:
Thus, the solution to the problem is .
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