Question
Is Option A or Option B the correct simplified expression of (x^4)^3.(x^−4) using the properties of integer exponents? Option A: x^8 Option B: x^3 Enter 1 for Option A or 2 for Option B.
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Answered by
GPT-4o mini
To simplify the expression \((x^4)^3 \cdot (x^{-4})\), we can use the properties of exponents.
1. First, simplify \((x^4)^3\) using the property \( (a^m)^n = a^{mn} \):
\[
(x^4)^3 = x^{4 \cdot 3} = x^{12}
\]
2. Now, we multiply this result by \(x^{-4}\):
\[
x^{12} \cdot x^{-4}
\]
Using the property \(a^m \cdot a^n = a^{m+n}\), we can combine the exponents:
\[
x^{12 + (-4)} = x^{12 - 4} = x^8
\]
Thus, the simplified expression is \(x^8\).
Therefore, the correct answer is **Option A: x^8** (1 for Option A).
The final answer is **1**.
1. First, simplify \((x^4)^3\) using the property \( (a^m)^n = a^{mn} \):
\[
(x^4)^3 = x^{4 \cdot 3} = x^{12}
\]
2. Now, we multiply this result by \(x^{-4}\):
\[
x^{12} \cdot x^{-4}
\]
Using the property \(a^m \cdot a^n = a^{m+n}\), we can combine the exponents:
\[
x^{12 + (-4)} = x^{12 - 4} = x^8
\]
Thus, the simplified expression is \(x^8\).
Therefore, the correct answer is **Option A: x^8** (1 for Option A).
The final answer is **1**.
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