Rewrite the expression (11^2)^8 as 11 to a single power.
Understand the Problem
The question asks to rewrite the expression (11^2)^8 as 11 to a single power. This involves applying the power of a power rule, which states that (a^m)^n = a^(m*n). We need to multiply the exponents to find the final power of 11.
Answer
$11^{16}$
Answer for screen readers
$11^{16}$
Steps to Solve
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Identify the rule to apply The problem involves a power raised to another power. The rule for this is $(a^m)^n = a^{m \cdot n}$.
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Apply the power of a power rule In this case, we have $(11^2)^8$. Applying the rule, we get $11^{2 \cdot 8}$.
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Multiply the exponents Multiply the exponents 2 and 8: $2 \cdot 8 = 16$.
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Write the result So, $(11^2)^8 = 11^{16}$.
$11^{16}$
More Information
The power of a power rule is a fundamental concept in algebra and is used extensively in simplifying expressions and solving equations involving exponents.
Tips
A common mistake is adding the exponents instead of multiplying them. Remember, $(a^m)^n = a^{m \cdot n}$ and not $a^{m+n}$.
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