Evaluating expressions with exponents requires carefully applying order of operations rules and exponent properties. When an exponential expression is nested inside another exponential expression, we need to evaluate from the innermost exponent working outwards. In this post, we’ll evaluate the expression (2x)^2, explaining each step in the process. We’ll also discuss strategies and insights on working with exponents nested within exponents.

## What is (2x)² when u do power to a power?

*When you raise (2x)² to a power, you multiply the exponents, resulting in (2x)⁴. This means you’ll have four factors of 2x multiplied together: (2x)(2x)(2x)(2x), which simplifies to 16x⁴.*

Certainly! Here’s a table that shows the step-by-step calculation of (2x)² when you raise a power to a power:

Expression | Calculation | Result |
---|---|---|

(2x)² | (2x)(2x) | 4x² |

## Reviewing Exponent Rules

Let’s first review some key rules and properties of exponents that are relevant:

- Follow PEMDAS order – Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
- To multiply with the same base, add the exponents. Example: x^3 * x^5 = x^8.
- An exponent applies only to the factor immediately before it.
- Evaluate exponents inside parentheses before applying outer exponents.

Keeping these facts in mind, let’s evaluate the expression (2x)^2.

## Evaluating (2x)^2 Step-by-Step

Following PEMDAS order:

- Evaluate innermost exponent first: (2x)^2
- (2x)^2 = (2x) * (2x)
- Apply outer exponent: (2x * 2x)
- Simplify like base terms: 2^2x^2

Therefore, the order of operations gives (2x)^2 = 2^2x^2 as the final simplified expression.

## Explanation

- The innermost exponent on 2x is evaluated first.
- The outer exponent means to multiply (2x) by itself.
- Multiplying terms with the same base 2x gives the product 2^2x^2.

This demonstrates the importance of methodical step-by-step application of PEMDAS and exponent rules.

## Strategies for Evaluating Complex Exponents

Some tips for exponents within exponents:

- Clearly identify the order and sequence of operations to perform.
- Evaluate inner exponents moving outwards following PEMDAS.
- Break into chunks and simplify nested sections first.
- Use parentheses around unclear sections.
- Double check work against exponent multiplication rules.

## Conclusion

In this post, we evaluated the exponential expression (2x)^2 step-by-step following proper order of operations and rules for exponents. Taking the time to show clear reasoning reinforces good practices for evaluating complex nested exponents systematically. Consistent practice builds familiarity with exponent notation, properties, and evaluation procedures. Fluency applying exponents provides the foundation for algebraic manipulation, calculus, statistics, and other advanced STEM fields relying on exponential functions. Be patient and keep persevering through those intricate exponents!

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