The Steps For Simplifying (2m45)3 Are Shown. Match The Properties To The Steps They Justify. Drag And Drop Application. (2m45)3=(2m4)353 (2m45)3=(2m4)353 Drop Zone Empty. (2m4)353=23(m4)353 (2m4)353=23(m4)353 Drop Zone Empty. 23(m4)353=8m12125

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The Steps for Simplifying (2m45)3: A Drag and Drop Application

In mathematics, simplifying algebraic expressions is a crucial skill that helps us solve equations and inequalities. One of the most common methods of simplification is by applying the properties of exponents. In this article, we will explore the steps for simplifying the expression (2m45)3 using a drag and drop application. We will match the properties to the steps they justify and provide a step-by-step guide on how to simplify the expression.

Step 1: Apply the Power Rule

The first step in simplifying (2m45)3 is to apply the power rule, which states that (an)m = an × m. In this case, we have (2m45)3, which can be rewritten as (2m45) × (2m45) × (2m45).

Step 2: Apply the Product Rule

The next step is to apply the product rule, which states that a × b × c = (a × b) × c. In this case, we can rewrite (2m45) × (2m45) × (2m45) as ((2m45) × (2m45)) × (2m45).

Step 3: Apply the Power Rule Again

Now, we can apply the power rule again to simplify ((2m45) × (2m45)) × (2m45). This can be rewritten as (2m45)2 × (2m45).

Step 4: Apply the Product Rule Again

Next, we can apply the product rule again to simplify (2m45)2 × (2m45). This can be rewritten as (2m45) × (2m45) × (2m45).

Step 5: Simplify Using the Properties of Exponents

Now, we can simplify (2m45) × (2m45) × (2m45) using the properties of exponents. We can rewrite this expression as (2m45)3.

Step 6: Apply the Power Rule One Last Time

Finally, we can apply the power rule one last time to simplify (2m45)3. This can be rewritten as (2m4)35.

Step 7: Simplify Using the Properties of Exponents Again

Now, we can simplify (2m4)35 using the properties of exponents. We can rewrite this expression as 23(m4)353.

Step 8: Simplify Using the Properties of Exponents Again

Next, we can simplify 23(m4)353 using the properties of exponents. We can rewrite this expression as 8m12125.

In conclusion, simplifying (2m45)3 using a drag and drop application involves applying the power rule, product rule, and properties of exponents. By following these steps, we can simplify the expression and arrive at the final answer of 8m12125.

  • What are some other methods for simplifying algebraic expressions?
  • How can we apply the power rule and product rule to simplify more complex expressions?
  • What are some common properties of exponents that we can use to simplify expressions?
  • The steps for simplifying (2m45)3 are:
    1. Apply the power rule: (2m45)3 = (2m45) × (2m45) × (2m45)
    2. Apply the product rule: ((2m45) × (2m45)) × (2m45)
    3. Apply the power rule again: (2m45)2 × (2m45)
    4. Apply the product rule again: (2m45) × (2m45) × (2m45)
    5. Simplify using the properties of exponents: (2m45)3
    6. Apply the power rule one last time: (2m4)35
    7. Simplify using the properties of exponents again: 23(m4)353
    8. Simplify using the properties of exponents again: 8m12125
  • Some other methods for simplifying algebraic expressions include:
    • Factoring
    • Canceling out common factors
    • Using the distributive property
  • We can apply the power rule and product rule to simplify more complex expressions by:
    • Breaking down the expression into smaller parts
    • Applying the power rule and product rule to each part
    • Simplifying the expression using the properties of exponents
      Q&A: Simplifying Algebraic Expressions

In our previous article, we explored the steps for simplifying the expression (2m45)3 using a drag and drop application. We matched the properties to the steps they justify and provided a step-by-step guide on how to simplify the expression. In this article, we will answer some of the most frequently asked questions about simplifying algebraic expressions.

Q: What are some common properties of exponents that we can use to simplify expressions?

A: There are several common properties of exponents that we can use to simplify expressions. Some of the most important ones include:

  • Power Rule: (an)m = an × m
  • Product Rule: a × b × c = (a × b) × c
  • Quotient Rule: (an)/(bm) = an × bm
  • Zero Exponent Rule: a0 = 1
  • Negative Exponent Rule: a-n = 1/an

Q: How can we apply the power rule and product rule to simplify more complex expressions?

A: To apply the power rule and product rule to simplify more complex expressions, we can follow these steps:

  1. Break down the expression into smaller parts: Divide the expression into smaller parts that can be simplified separately.
  2. Apply the power rule and product rule to each part: Use the power rule and product rule to simplify each part of the expression.
  3. Simplify the expression using the properties of exponents: Use the properties of exponents to simplify the expression.

Q: What are some other methods for simplifying algebraic expressions?

A: Some other methods for simplifying algebraic expressions include:

  • Factoring: Breaking down an expression into simpler factors.
  • Canceling out common factors: Canceling out common factors in an expression.
  • Using the distributive property: Using the distributive property to simplify an expression.

Q: How can we use the distributive property to simplify an expression?

A: To use the distributive property to simplify an expression, we can follow these steps:

  1. Distribute the terms: Distribute the terms in the expression to each of the factors.
  2. Combine like terms: Combine like terms in the expression.
  3. Simplify the expression: Simplify the expression using the properties of exponents.

Q: What are some common mistakes to avoid when simplifying algebraic expressions?

A: Some common mistakes to avoid when simplifying algebraic expressions include:

  • Forgetting to apply the power rule and product rule: Forgetting to apply the power rule and product rule can lead to incorrect simplifications.
  • Not combining like terms: Not combining like terms can lead to incorrect simplifications.
  • Not using the distributive property: Not using the distributive property can lead to incorrect simplifications.

In conclusion, simplifying algebraic expressions is a crucial skill that requires a deep understanding of the properties of exponents and the rules of algebra. By following the steps outlined in this article, we can simplify complex expressions and arrive at the final answer. Remember to avoid common mistakes and use the distributive property to simplify expressions.

  • What are some other methods for simplifying algebraic expressions?
  • How can we apply the power rule and product rule to simplify more complex expressions?
  • What are some common properties of exponents that we can use to simplify expressions?
  • Some other methods for simplifying algebraic expressions include:
    • Factoring
    • Canceling out common factors
    • Using the distributive property
  • We can apply the power rule and product rule to simplify more complex expressions by:
    • Breaking down the expression into smaller parts
    • Applying the power rule and product rule to each part
    • Simplifying the expression using the properties of exponents
  • Some common properties of exponents that we can use to simplify expressions include:
    • Power Rule: (an)m = an × m
    • Product Rule: a × b × c = (a × b) × c
    • Quotient Rule: (an)/(bm) = an × bm
    • Zero Exponent Rule: a0 = 1
    • Negative Exponent Rule: a-n = 1/an