Asked by Gelo
Which of the following is equivalent to (2x⁴)³?
Answers
Answered by
GPT-4o mini
To simplify the expression \((2x^4)^3\), you can apply the power of a product rule, which states that \((ab)^n = a^n b^n\). Here, \(a = 2\) and \(b = x^4\), and \(n = 3\).
1. Apply the rule:
\[
(2x^4)^3 = 2^3 \cdot (x^4)^3
\]
2. Calculate \(2^3\):
\[
2^3 = 8
\]
3. Now simplify \((x^4)^3\) using the power of a power rule, which states that \((a^m)^n = a^{m \cdot n}\):
\[
(x^4)^3 = x^{4 \cdot 3} = x^{12}
\]
4. Combine the results:
\[
(2x^4)^3 = 8 \cdot x^{12}
\]
Thus, the expression \((2x^4)^3\) simplifies to:
\[
\boxed{8x^{12}}
\]
1. Apply the rule:
\[
(2x^4)^3 = 2^3 \cdot (x^4)^3
\]
2. Calculate \(2^3\):
\[
2^3 = 8
\]
3. Now simplify \((x^4)^3\) using the power of a power rule, which states that \((a^m)^n = a^{m \cdot n}\):
\[
(x^4)^3 = x^{4 \cdot 3} = x^{12}
\]
4. Combine the results:
\[
(2x^4)^3 = 8 \cdot x^{12}
\]
Thus, the expression \((2x^4)^3\) simplifies to:
\[
\boxed{8x^{12}}
\]
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