Math Problem Statement
Simplify the expression (2m5)6 .
Solution
To simplify the expression , follow these steps:
Step 1: Apply the Power of a Product Rule
The power of a product rule states that . In this case, you can apply it to both the constant and the variable term :
Step 2: Simplify Each Term
- For , use the power of a power rule, which states . So, .
Step 3: Write the Final Expression
Now combine everything:
Thus, the simplified expression is:
Would you like more details or have any questions?
Here are 5 related questions to expand on this:
- How would you simplify ?
- What happens when simplifying ?
- How does the power rule work when applying it to a negative exponent, e.g., ?
- How do you simplify a product of two powers, e.g., ?
- Can you explain how the product rule is applied to expressions with multiple terms?
Tip: When raising a product to a power, apply the exponent to each factor inside the parentheses.
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Math Problem Analysis
Mathematical Concepts
Exponents
Power of a Product Rule
Power of a Power Rule
Formulas
(ab)^n = a^n * b^n
(x^a)^b = x^{a * b}
Theorems
Laws of Exponents
Suitable Grade Level
Grades 8-10