Math Problem Statement
Solution
The question in the image asks for which of the following expressions are equivalent to . Let's go through the process of solving this step by step:
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Simplifying the given expression:
Using the rule of exponents , we can add the exponents:
The goal now is to see which of the listed options are equivalent to .
Examining the options:
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Option 1:
This is exactly equal to , so this option is correct.
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Option 2:
Using the exponent rule , we get:
This is also equivalent to , so this option is correct.
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Option 3:
Simplifying , where , we get:
This is not equal to , so this option is incorrect.
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Option 4:
This represents two separate terms: and . Adding them does not combine exponents, so this is not equivalent to . Hence, this option is incorrect.
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Option 5:
Simplifying inside the cube root:
Now applying the cube root:
This is equivalent to , so this option is correct.
Correct answers:
- Option 1:
- Option 2:
- Option 5:
Would you like further details on any part of the process?
Here are 5 related questions to consider:
- How do exponent rules apply to combining terms with the same base?
- What is the general rule for simplifying expressions inside radicals?
- How can you recognize when two expressions are equivalent using exponent laws?
- What is the importance of cube roots in simplifying radical expressions?
- How do fractional exponents relate to radicals?
Tip: Always look for exponent laws like and to simplify terms efficiently.
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Math Problem Analysis
Mathematical Concepts
Exponents
Radicals
Simplification
Formulas
a^m * a^n = a^(m+n)
(a^m)^n = a^(m*n)
Cube root of a = a^(1/3)
Theorems
Exponent Multiplication Rule
Exponent Power Rule
Suitable Grade Level
Grades 9-11