Rewrite The Expression With The Assumption That Variables Are Not Zero: 17 Z − 3 17 Z^{-3} 17 Z − 3

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Introduction

In mathematics, expressions involving negative exponents are common, especially when dealing with variables. When we encounter an expression with a negative exponent, it is essential to rewrite it in a more manageable form. In this article, we will focus on rewriting the expression $17 z^{-3}$ with the assumption that variables are not zero.

Understanding Negative Exponents

A negative exponent is a mathematical operation that involves raising a number to a power that is less than zero. In the expression $17 z^{-3}$, the variable $z$ is raised to the power of $-3$. To rewrite this expression, we need to understand the concept of negative exponents and how they can be manipulated.

Rewriting Negative Exponents

When we have a negative exponent, we can rewrite it as a positive exponent by taking the reciprocal of the base and changing the sign of the exponent. In other words, if we have an expression of the form $a^{-n}$, we can rewrite it as $\frac{1}{a^n}$. This is a fundamental property of exponents that allows us to simplify expressions involving negative exponents.

Applying the Property to the Given Expression

Now that we have understood the concept of negative exponents and how to rewrite them, let's apply this property to the given expression $17 z^{-3}$. We can rewrite this expression as follows:

$$17 z^{-3} = \frac{17}{z^3}$$

In this rewritten form, we have taken the reciprocal of the base $z$ and changed the sign of the exponent from negative to positive.

Simplifying the Expression

The rewritten expression $\frac{17}{z^3}$ can be further simplified by expressing the denominator as a product of three identical factors. This can be done by using the property of exponents that states $a^m \cdot a^n = a^{m+n}$. In this case, we can rewrite the denominator as follows:

$$z^3 = z \cdot z \cdot z$$

Now, we can substitute this expression into the rewritten form of the original expression:

$$\frac{17}{z^3} = \frac{17}{z \cdot z \cdot z}$$

Final Simplification

The expression $\frac{17}{z \cdot z \cdot z}$ can be further simplified by canceling out the common factors in the numerator and denominator. In this case, we can cancel out the factor of $z$ in the numerator and denominator:

$$\frac{17}{z \cdot z \cdot z} = \frac{17}{z^3}$$

However, we can simplify this expression further by expressing the denominator as a product of three identical factors:

$$\frac{17}{z^3} = \frac{17}{z \cdot z \cdot z}$$

Conclusion

In this article, we have rewritten the expression $17 z^{-3}$ with the assumption that variables are not zero. We have applied the property of negative exponents to rewrite the expression as a positive exponent and then simplified the resulting expression. The final simplified form of the expression is $\frac{17}{z \cdot z \cdot z}$.

Key Takeaways

• Negative exponents can be rewritten as positive exponents by taking the reciprocal of the base and changing the sign of the exponent.
• The property of negative exponents can be applied to simplify expressions involving negative exponents.
• The final simplified form of the expression $17 z^{-3}$ is $\frac{17}{z \cdot z \cdot z}$.

Further Reading

For more information on negative exponents and how to rewrite them, we recommend checking out the following resources:

• Khan Academy: Negative Exponents
• Mathway: Negative Exponents
• Wolfram MathWorld: Negative Exponents

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Introduction

In our previous article, we discussed how to rewrite expressions with negative exponents. We applied the property of negative exponents to simplify the expression $17 z^{-3}$ and arrived at the final simplified form of $\frac{17}{z \cdot z \cdot z}$. In this article, we will answer some frequently asked questions related to rewriting expressions with negative exponents.

Q: What is the property of negative exponents?

A: The property of negative exponents states that if we have an expression of the form $a^{-n}$, we can rewrite it as $\frac{1}{a^n}$. This means that we can take the reciprocal of the base and change the sign of the exponent to rewrite a negative exponent as a positive exponent.

Q: How do I apply the property of negative exponents to rewrite an expression?

A: To apply the property of negative exponents, simply take the reciprocal of the base and change the sign of the exponent. For example, if we have the expression $a^{-3}$, we can rewrite it as $\frac{1}{a^3}$.

Q: Can I simplify an expression with a negative exponent further?

A: Yes, you can simplify an expression with a negative exponent further by expressing the denominator as a product of identical factors. For example, if we have the expression $\frac{1}{a^3}$, we can rewrite it as $\frac{1}{a \cdot a \cdot a}$.

Q: What if the expression has multiple negative exponents?

A: If the expression has multiple negative exponents, you can apply the property of negative exponents to each exponent separately. For example, if we have the expression $a^{-3} \cdot b^{-2}$, we can rewrite it as $\frac{1}{a^3} \cdot \frac{1}{b^2}$.

Q: Can I rewrite an expression with a negative exponent as a fraction with a negative exponent in the denominator?

A: Yes, you can rewrite an expression with a negative exponent as a fraction with a negative exponent in the denominator. For example, if we have the expression $a^{-3}$, we can rewrite it as $\frac{1}{a^3}$, which is equivalent to $\frac{1}{a^{-3}}$.

Q: What if the expression has a negative exponent and a variable in the denominator?

A: If the expression has a negative exponent and a variable in the denominator, you can apply the property of negative exponents to rewrite the expression. For example, if we have the expression $\frac{1}{x^3}$, we can rewrite it as $\frac{1}{x \cdot x \cdot x}$.

Q: Can I rewrite an expression with a negative exponent as a decimal or a percentage?

A: Yes, you can rewrite an expression with a negative exponent as a decimal or a percentage. For example, if we have the expression $a^{-3}$, we can rewrite it as $\frac{1}{a^3}$, which is equivalent to $0.001$ or $0.1\%$.

Conclusion

In this article, we have answered some frequently asked questions related to rewriting expressions with negative exponents. We have discussed the property of negative exponents, how to apply it to rewrite expressions, and how to simplify expressions with multiple negative exponents. By following the steps outlined in this article, you should be able to rewrite expressions with negative exponents with confidence.

Key Takeaways

• The property of negative exponents states that if we have an expression of the form $a^{-n}$, we can rewrite it as $\frac{1}{a^n}$.
• To apply the property of negative exponents, simply take the reciprocal of the base and change the sign of the exponent.
• You can simplify an expression with a negative exponent further by expressing the denominator as a product of identical factors.
• You can rewrite an expression with a negative exponent as a fraction with a negative exponent in the denominator.
• You can rewrite an expression with a negative exponent as a decimal or a percentage.

Further Reading

For more information on negative exponents and how to rewrite them, we recommend checking out the following resources:

• Khan Academy: Negative Exponents
• Mathway: Negative Exponents
• Wolfram MathWorld: Negative Exponents

By following the steps outlined in this article, you should be able to rewrite expressions with negative exponents with confidence. Remember to apply the property of negative exponents and simplify the resulting expression to get the final answer.