We appreciate your visit to Exponent Rules 21 Simplify tex x 3 times x 4 tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
- Identify the common base: $x$.
- Apply the exponent rule for multiplication: $x^m
\cdot x^n = x^{m+n}$.
- Add the exponents: $3 + 4 = 7$.
- Simplify the expression: $\boxed{x^7}$.
### Explanation
1. Understanding the problem
We are asked to simplify the expression $x^3 \cdot x^4$. This involves using the rules of exponents. Specifically, when multiplying two terms with the same base, we add their exponents.
2. Applying the exponent rule
The rule for multiplying exponents with the same base is: $$a^m \cdot a^n = a^{m+n}$$ In our case, the base is $x$, and the exponents are $3$ and $4$.
3. Simplifying the expression
Adding the exponents, we have:$$3 + 4 = 7$$Therefore, the simplified expression is:$$x^3 \cdot x^4 = x^{3+4} = x^7$$
4. Final Answer
The simplified form of $x^3 \cdot x^4$ is $x^7$.
### Examples
Exponent rules are fundamental in many areas of mathematics and science. For example, in physics, when calculating the volume of a cube with side length $x$, if the side length doubles, the volume becomes $(2x)^3 = 8x^3$, which shows how the exponent affects the final result. Similarly, in computer science, exponents are used to describe the growth rate of algorithms, such as $O(n^2)$ or $O(2^n)$, where $n$ is the input size. Understanding exponent rules helps in analyzing and comparing the efficiency of different algorithms.
- Apply the exponent rule for multiplication: $x^m
\cdot x^n = x^{m+n}$.
- Add the exponents: $3 + 4 = 7$.
- Simplify the expression: $\boxed{x^7}$.
### Explanation
1. Understanding the problem
We are asked to simplify the expression $x^3 \cdot x^4$. This involves using the rules of exponents. Specifically, when multiplying two terms with the same base, we add their exponents.
2. Applying the exponent rule
The rule for multiplying exponents with the same base is: $$a^m \cdot a^n = a^{m+n}$$ In our case, the base is $x$, and the exponents are $3$ and $4$.
3. Simplifying the expression
Adding the exponents, we have:$$3 + 4 = 7$$Therefore, the simplified expression is:$$x^3 \cdot x^4 = x^{3+4} = x^7$$
4. Final Answer
The simplified form of $x^3 \cdot x^4$ is $x^7$.
### Examples
Exponent rules are fundamental in many areas of mathematics and science. For example, in physics, when calculating the volume of a cube with side length $x$, if the side length doubles, the volume becomes $(2x)^3 = 8x^3$, which shows how the exponent affects the final result. Similarly, in computer science, exponents are used to describe the growth rate of algorithms, such as $O(n^2)$ or $O(2^n)$, where $n$ is the input size. Understanding exponent rules helps in analyzing and comparing the efficiency of different algorithms.
Thanks for taking the time to read Exponent Rules 21 Simplify tex x 3 times x 4 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
