Select The Correct Answer.What Is The Value Of This Expression If $h=8$, $j=-1$, And $k=-12$?$\frac{j^3 K}{h^0}$A. -12 B. $\frac{3}{2}$ C. 36 D. 12

When evaluating expressions with exponents and variables, it's essential to understand the rules of exponentiation and how to substitute values into the expression. In this article, we'll explore how to evaluate the expression $\frac{j^3 k}{h^0}$ given the values of $h$, $j$, and $k$.

Understanding Exponents

Exponents are a shorthand way of writing repeated multiplication. For example, $a^3$ means $a \times a \times a$. When evaluating expressions with exponents, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Evaluating the Expression

Given the expression $\frac{j^3 k}{h^0}$, we need to substitute the values of $h$, $j$, and $k$ into the expression. We're given that $h=8$, $j=-1$, and $k=-12$.

First, let's evaluate the exponent $h^0$. Any number raised to the power of 0 is equal to 1, so $h^0 = 1$.

Next, let's evaluate the exponent $j^3$. We need to raise $j$ to the power of 3, which means multiplying $j$ by itself three times: $j^3 = (-1) \times (-1) \times (-1) = -1$.

Now, let's substitute the values of $h$, $j$, and $k$ into the expression:

$$\frac{j^3 k}{h^0} = \frac{(-1) \times (-12)}{1}$$

Simplifying the expression, we get:

$$\frac{j^3 k}{h^0} = 12$$

Conclusion

In this article, we evaluated the expression $\frac{j^3 k}{h^0}$ given the values of $h$, $j$, and $k$. We followed the order of operations and substituted the values into the expression. The final answer is $\boxed{12}$.

Discussion

Do you have any questions about evaluating expressions with exponents and variables? Share your thoughts in the comments below!

Additional Resources

If you're struggling with exponents or need more practice, here are some additional resources:

• Khan Academy: Exponents
• Mathway: Exponents and Variables
• IXL: Exponents and Variables

Final Answer

In our previous article, we explored how to evaluate the expression $\frac{j^3 k}{h^0}$ given the values of $h$, $j$, and $k$. We followed the order of operations and substituted the values into the expression. In this article, we'll answer some common questions about evaluating expressions with exponents and variables.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The order of operations is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the rule for exponents?

A: The rule for exponents is that any number raised to the power of 0 is equal to 1. For example, $a^0 = 1$.

Q: How do I evaluate an expression with multiple exponents?

A: When evaluating an expression with multiple exponents, we need to follow the order of operations. We need to evaluate any exponential expressions first, and then perform any multiplication and division operations from left to right.

Q: What is the difference between $h^2$ and $h \times h$?

A: $h^2$ means $h$ raised to the power of 2, which means $h$ multiplied by itself. For example, $h^2 = h \times h$. On the other hand, $h \times h$ means $h$ multiplied by $h$, but it does not have an exponent.

Q: Can I simplify an expression with exponents?

A: Yes, we can simplify an expression with exponents by combining like terms. For example, if we have the expression $2x^2 + 3x^2$, we can combine the like terms to get $5x^2$.

Q: How do I evaluate an expression with negative exponents?

A: When evaluating an expression with negative exponents, we need to follow the rule that any number raised to the power of -1 is equal to the reciprocal of the number. For example, $a^{-1} = \frac{1}{a}$.

Q: Can I evaluate an expression with variables and exponents?

A: Yes, we can evaluate an expression with variables and exponents by substituting the values of the variables into the expression and following the order of operations.

Q: What is the final answer to the expression $\frac{j^3 k}{h^0}$?

A: The final answer to the expression $\frac{j^3 k}{h^0}$ is $\boxed{12}$.

Conclusion

In this article, we answered some common questions about evaluating expressions with exponents and variables. We covered the order of operations, the rule for exponents, and how to evaluate expressions with multiple exponents, negative exponents, and variables. We also provided some examples to illustrate the concepts.

Discussion

Do you have any questions about evaluating expressions with exponents and variables? Share your thoughts in the comments below!

Additional Resources

If you're struggling with exponents or need more practice, here are some additional resources:

• Khan Academy: Exponents
• Mathway: Exponents and Variables
• IXL: Exponents and Variables

Final Answer

The final answer is $\boxed{12}$.