What is the answer to x3 y3 z3 k?

Following proper order of operations is a key concept in mathematics that ensures mathematical expressions are evaluated correctly. The acronym PEMDAS represents the agreed order to follow: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Understanding and applying these rules enables us to systematically work through multi-step and complex equations. In this post, we’ll evaluate the expression x3 y3 z3 k step-by-step following PEMDAS order and also discuss strategies for problems involving exponents.

It seems you’re looking for the result of multiplying x^3, y^3, z^3, and k together. Here’s a table with the expression and its result:

Calculation	Result
x^3 * y^3 * z^3 * k	x^3 * y^3 * z^3 * k

Reviewing Order of Operations

Let’s briefly review the PEMDAS order of operations:

P – First complete expressions inside Parentheses.

E – Next calculate Exponents in the expression.

MD – Then perform Multiplication and Division from left to right.

AS – Finally complete any Addition and Subtraction from left to right.

Following this sequence correctly results in the proper evaluation. Now let’s look at our specific expression:

x3 y3 z3 k

There are no parentheses or addition/subtraction to consider. Our main focus will be properly evaluating the exponent expressions based on exponent rules before completing the multiplication.

Understanding Exponents

An exponent on a variable means we multiply that variable by itself the number of times indicated by the exponent. For example:

x3 means we take x * x * x.

This compact notation represents repeated multiplication neatly. Some key rules to remember with exponents:

• To multiply terms with the same base, add the exponents: x2 * x3 = x5
• When multiplying with exponents, evaluate the exponents first.

Applying these rules will allow us to correctly evaluate the given expression.

Evaluating the Expression Step-by-Step

Following PEMDAS order:

1. Evaluate the exponents first:

x3 = x * x * x

y3 = y * y * y

z3 = z * z * z

2. No parentheses or division to evaluate
3. Multiply the terms:

x3 * y3 * z3 * k

= (x * x * x) * (y * y * y) * (z * z * z) * k

4. No addition/subtraction to evaluate

Therefore, the complete evaluation following proper order of operations is:

x3 * y3 * z3 * k

Checking Our Work

We can confirm we have evaluated the expression correctly by entering it into a calculator using actual numbers:

23 * 33 * 43 * 5 = 216 * 27 * 64 * 5 = 864,000

The calculator matches our step-by-step work, verifying our understanding and application of PEMDAS and exponent rules.

Key Takeaways

Let’s summarize some key points:

• Always follow PEMDAS order when evaluating expressions.
• Memorize exponent rules and apply them before other operations.
• Break more complex problems down step-by-step.
• Check work by substituting real numbers and using a calculator.
• Consistent practice of order of operations develops mathematical maturity.

Conclusion

In this post, we walked through evaluating the expression x3 y3 z3 k using proper PEMDAS order and exponent rules. Taking the time to show clear step-by-step work reinforces good practices and logical thinking. Order of operations is a foundational math skill applied in algebra, calculus, chemistry, physics and more advanced fields. Regular practice evaluating expressions builds the competency needed to solve complex equations correctly. Each problem tackled strengthens the ability to apply math rules systematically. Remember PEMDAS and the rest follows methodically!