Simplify. Assume All Variables Are Positive. U 7 4 U 1 4 \frac{u^{\frac{7}{4}}}{u^{\frac{1}{4}}} U 4 1 ​ U 4 7 ​ ​ Write Your Answer In The Form A A A Or A B \frac{A}{B} B A ​ Where A A A And B B B Are Constants Or Variables That Have No Variables In

Simplify the Expression: $\frac{u^{\frac{7}{4}}}{u^{\frac{1}{4}}}$

In mathematics, simplifying expressions is an essential skill that helps us solve problems efficiently. When dealing with exponents, we need to apply the rules of exponentiation to simplify the expression. In this article, we will simplify the expression $\frac{u^{\frac{7}{4}}}{u^{\frac{1}{4}}}$ using the rules of exponentiation.

Before we simplify the expression, let's understand the concept of exponents. An exponent is a small number that is written above and to the right of a number or a variable. It represents the power to which the base is raised. For example, in the expression $u^{\frac{7}{4}}$, the exponent $\frac{7}{4}$ represents the power to which the base $u$ is raised.

To simplify the expression $\frac{u^{\frac{7}{4}}}{u^{\frac{1}{4}}}$, we can use the rule of exponentiation that states $\frac{a^m}{a^n} = a^{m-n}$, where $a$ is a positive number or a variable, and $m$ and $n$ are integers.

Using this rule, we can rewrite the expression as:

$$\frac{u^{\frac{7}{4}}}{u^{\frac{1}{4}}} = u^{\frac{7}{4} - \frac{1}{4}}$$

Now, let's simplify the exponent:

$$\frac{7}{4} - \frac{1}{4} = \frac{6}{4} = \frac{3}{2}$$

So, the simplified expression is:

$$u^{\frac{3}{2}}$$

In this article, we simplified the expression $\frac{u^{\frac{7}{4}}}{u^{\frac{1}{4}}}$ using the rules of exponentiation. We applied the rule $\frac{a^m}{a^n} = a^{m-n}$ to simplify the expression and obtained the final result $u^{\frac{3}{2}}$. This result can be further simplified to $\sqrt{u^3}$, but we will leave it in the form $u^{\frac{3}{2}}$.

The final answer is $\boxed{u^{\frac{3}{2}}}$.
Simplify the Expression: $\frac{u^{\frac{7}{4}}}{u^{\frac{1}{4}}}$ - Q&A

In our previous article, we simplified the expression $\frac{u^{\frac{7}{4}}}{u^{\frac{1}{4}}}$ using the rules of exponentiation. In this article, we will answer some frequently asked questions related to the simplification of this expression.

Q: What is the rule of exponentiation used to simplify the expression?

A: The rule of exponentiation used to simplify the expression is $\frac{a^m}{a^n} = a^{m-n}$, where $a$ is a positive number or a variable, and $m$ and $n$ are integers.

Q: Can you explain why we can rewrite the expression as $u^{\frac{7}{4} - \frac{1}{4}}$?

A: Yes, we can rewrite the expression as $u^{\frac{7}{4} - \frac{1}{4}}$ because the rule of exponentiation states that we can subtract the exponents when dividing two powers with the same base.

Q: How do we simplify the exponent $\frac{7}{4} - \frac{1}{4}$?

A: To simplify the exponent $\frac{7}{4} - \frac{1}{4}$, we can subtract the numerators and keep the denominator the same. This gives us $\frac{6}{4}$, which can be further simplified to $\frac{3}{2}$.

Q: What is the final simplified expression?

A: The final simplified expression is $u^{\frac{3}{2}}$.

Q: Can you explain why we can write $u^{\frac{3}{2}}$ as $\sqrt{u^3}$?

A: Yes, we can write $u^{\frac{3}{2}}$ as $\sqrt{u^3}$ because the exponent $\frac{3}{2}$ can be written as $3 \times \frac{1}{2}$, which is equivalent to taking the square root of $u^3$.

Q: What are some common mistakes to avoid when simplifying expressions with exponents?

A: Some common mistakes to avoid when simplifying expressions with exponents include:

• Not applying the rule of exponentiation correctly
• Not simplifying the exponent correctly
• Not checking if the base is positive or negative
• Not considering the order of operations

In this article, we answered some frequently asked questions related to the simplification of the expression $\frac{u^{\frac{7}{4}}}{u^{\frac{1}{4}}}$. We explained the rule of exponentiation used to simplify the expression, simplified the exponent, and provided some common mistakes to avoid when simplifying expressions with exponents.

The final answer is $\boxed{u^{\frac{3}{2}}}$.