Simplify The Expression:$\[ -14 X^3 Y^3 (16 X^3) \\]

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Understanding the Expression

The given expression is $-14 x^3 y^3 (16 x^3)$. This expression involves variables $x$ and $y$ and constants $-14$ and $16$. To simplify the expression, we need to apply the rules of exponents and combine like terms.

Applying the Rules of Exponents

The expression contains two terms with the same base, $x^3$. When multiplying terms with the same base, we add the exponents. Therefore, we can simplify the expression as follows:

$$-14 x^3 y^3 (16 x^3) = -14 x^3 y^3 \cdot 16 x^3$$

Simplifying the Expression

Now, we can simplify the expression by multiplying the constants and adding the exponents of the variables.

$$-14 x^3 y^3 \cdot 16 x^3 = -14 \cdot 16 \cdot x^3 \cdot x^3 \cdot y^3$$

Combining Like Terms

We can combine the constants by multiplying them together.

$$-14 \cdot 16 = -224$$

Simplifying the Expression Further

Now, we can simplify the expression further by adding the exponents of the variables.

$$x^3 \cdot x^3 = x^{3+3} = x^6$$

Final Simplification

Therefore, the final simplified expression is:

$$-224 x^6 y^3$$

Conclusion

In this article, we simplified the expression $-14 x^3 y^3 (16 x^3)$ by applying the rules of exponents and combining like terms. We started by understanding the expression and identifying the variables and constants involved. Then, we applied the rules of exponents to simplify the expression and combined like terms to get the final simplified expression.

Frequently Asked Questions

• What is the simplified expression of $-14 x^3 y^3 (16 x^3)$?
• How do we simplify expressions involving variables and constants?
• What are the rules of exponents that we need to apply when simplifying expressions?

Answering the FAQs

• The simplified expression of $-14 x^3 y^3 (16 x^3)$ is $-224 x^6 y^3$.
• To simplify expressions involving variables and constants, we need to apply the rules of exponents, which state that when multiplying terms with the same base, we add the exponents.
• The rules of exponents that we need to apply when simplifying expressions are:
  • When multiplying terms with the same base, we add the exponents.
  • When dividing terms with the same base, we subtract the exponents.
  • When raising a term with a variable to a power, we multiply the exponent by the power.

Final Thoughts

Simplifying expressions is an essential skill in mathematics, and it requires a good understanding of the rules of exponents and how to combine like terms. By applying these rules and techniques, we can simplify complex expressions and make them easier to work with.

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Understanding the Expression

The given expression is $-14 x^3 y^3 (16 x^3)$. This expression involves variables $x$ and $y$ and constants $-14$ and $16$. To simplify the expression, we need to apply the rules of exponents and combine like terms.

Frequently Asked Questions

Q: What is the simplified expression of $-14 x^3 y^3 (16 x^3)$?

A: The simplified expression of $-14 x^3 y^3 (16 x^3)$ is $-224 x^6 y^3$.

Q: How do we simplify expressions involving variables and constants?

A: To simplify expressions involving variables and constants, we need to apply the rules of exponents, which state that when multiplying terms with the same base, we add the exponents.

Q: What are the rules of exponents that we need to apply when simplifying expressions?

A: The rules of exponents that we need to apply when simplifying expressions are: + When multiplying terms with the same base, we add the exponents. + When dividing terms with the same base, we subtract the exponents. + When raising a term with a variable to a power, we multiply the exponent by the power.

Q: Can we simplify expressions with negative exponents?

A: Yes, we can simplify expressions with negative exponents. When a term has a negative exponent, we can rewrite it as a fraction with a positive exponent. For example, $x^{-3}$ can be rewritten as $\frac{1}{x^3}$.

Q: How do we simplify expressions with fractional exponents?

A: To simplify expressions with fractional exponents, we need to apply the rules of exponents and the properties of fractions. For example, $(x^{\frac{1}{2}})^3$ can be simplified as $x^{\frac{3}{2}}$.

Q: Can we simplify expressions with variables in the denominator?

A: Yes, we can simplify expressions with variables in the denominator. When a term has a variable in the denominator, we can rewrite it as a fraction with a variable in the numerator. For example, $\frac{1}{x^3}$ can be rewritten as $x^{-3}$.

Q: How do we simplify expressions with multiple variables?

A: To simplify expressions with multiple variables, we need to apply the rules of exponents and combine like terms. For example, $x^3 y^3 (x^3 y^3)$ can be simplified as $x^6 y^6$.

Conclusion

In this article, we answered some frequently asked questions about simplifying expressions. We covered topics such as the rules of exponents, simplifying expressions with negative exponents, fractional exponents, variables in the denominator, and multiple variables. By applying these rules and techniques, we can simplify complex expressions and make them easier to work with.

Final Thoughts

Simplifying expressions is an essential skill in mathematics, and it requires a good understanding of the rules of exponents and how to combine like terms. By practicing and applying these rules and techniques, we can become proficient in simplifying expressions and make them easier to work with.

Additional Resources

• Rules of Exponents
• Simplifying Expressions
• Exponents and Powers

Related Articles

• Simplifying Expressions with Variables
• Simplifying Expressions with Fractions
• Simplifying Expressions with Negative Exponents