Complete the following exercise:
Complete the following exercise:
\( \sqrt{\sqrt{3x^2}}= \)
Complete the following exercise:
\( \sqrt{\sqrt{16\cdot x^2}}= \)
Complete the following exercise:
\( \sqrt{\sqrt{81\cdot x^4}}= \)
Complete the following exercise:
\( \sqrt[3]{\sqrt{64\cdot x^{12}}=} \)
Complete the following exercise:
\( \sqrt[8]{\sqrt{x^8}}= \)
Complete the following exercise:
To solve , follow these steps:
Therefore, the simplified form of the given expression is .
Complete the following exercise:
To solve the expression , follow these steps:
Therefore, the simplified form of is . This corresponds to choice 1.
Complete the following exercise:
To solve the problem , we need to simplify this expression using properties of exponents and square roots.
Therefore, the solution to the problem is .
Complete the following exercise:
To solve the problem , follow these detailed steps:
First, we need to find .
The square root of a product can be expressed as the product of the square roots: .
Simplifying further, we find:
Thus, the inner square root becomes .
Next, apply the cube root to the result of the inner square root: .
The cube root of a product can also be expressed as the product of the cube roots:
Thus, the expression simplifies to .
Therefore, the solution to this problem is , which corresponds to choice 2 in the provided options.
Complete the following exercise:
To solve the problem , we'll simplify the expression using exponent rules:
Thus, the expression simplifies to .
Complete the following exercise:
\( \sqrt[]{\sqrt{5x^4}}= \)
Comlete the following exercise:
\( \sqrt[10]{\sqrt{x^{20}}}= \)
Complete the following exercise:
\( \sqrt[5]{\sqrt{x^{20}}}= \)
Complete the following exercise:
\( \sqrt[6]{\sqrt{x^{12}}}= \)
Complete the following exercise:
\( \sqrt[6]{\sqrt{25x^6}} \)
Complete the following exercise:
To solve the expression , let's go step-by-step:
Therefore, the simplified expression is .
Comlete the following exercise:
To solve the problem, we'll simplify using properties of exponents and roots:
Therefore, the expression simplifies to .
Conclusion: The solution to the problem is .
Complete the following exercise:
To solve the problem , we will convert the roots into fractional exponents and simplify:
The expression can be represented as:
Now, taking the fifth root of , we have:
Therefore, the original expression simplifies to .
Complete the following exercise:
To solve , we will follow these steps:
Now, let's perform each of these steps:
Step 1: Simplify .
.
Step 2: Simplify the outer expression .
.
Step 3: Apply the exponent rule .
.
Therefore, the simplified expression is .
Thus, the solution to is .
Complete the following exercise:
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: We have the expression . Begin by simplifying the inner square root:
.
We know and .
So, .
Step 2: Apply the outer sixth root:
.
Convert as :
Since ,
we have .
Therefore, the solution becomes:
.
Therefore, the solution to the problem is .
Complete the following exercise:
\( \sqrt[4]{\sqrt[3]{49\cdot x}}= \)
Complete the following exercise:
\( \sqrt[3]{\sqrt{144x^3}}= \)
Complete the following exercise:
\( \sqrt[3]{\sqrt[3]{512x^{27}}}= \)
Solve the following exercise:
\( \sqrt{\sqrt{4x^{16}}}= \)
Complete the following exercise:
\( \sqrt[4]{\sqrt{100x}}= \)
Complete the following exercise:
To simplify the given expression , we will use the property of roots as fractional exponents.
Therefore, the solution to the problem is .
Complete the following exercise:
To solve the expression , let's proceed step by step:
Therefore, the simplified expression is , which corresponds to the third choice.
Complete the following exercise:
To solve the given problem, we'll follow these steps:
Let's go through each step:
Step 1: Consider the expression .
First, evaluate . Since , we have .
For , use the property :
.
Thus, .
Step 2: Now, evaluate the outer cube root .
since .
For , again use the rule :
.
Therefore, .
In conclusion, the simplified expression is .
Thus, the solution to the problem is , which corresponds to choice 3.
Solve the following exercise:
Complete the following exercise: