Question
Simplify the expression(4x power of 3) and then outside of the parentheses power of two using the properties of integer exponents. Would the answer be eight times power 64 times power of six times power of six or 16 times power of five.
Answers
GPT-4o mini
To simplify the expression \((4x^3)^2\), we will use the properties of exponents.
1. First, apply the power of a product rule, which states that \((ab)^n = a^n b^n\). In this case, \(a = 4\) and \(b = x^3\):
\[
(4x^3)^2 = 4^2 (x^3)^2
\]
2. Now calculate \(4^2\) and \((x^3)^2\):
\[
4^2 = 16 \quad \text{and} \quad (x^3)^2 = x^{3 \cdot 2} = x^6
\]
3. Bringing everything together:
\[
(4x^3)^2 = 16x^6
\]
Now we have simplified \((4x^3)^2\) to \(16x^6\).
Regarding your question about whether the answer is \(8 \times 64 \times 6^6\) or \(16 \times 5\), the correct simplified expression is **neither**. The simplification of the original expression is \(16x^6\).
1. First, apply the power of a product rule, which states that \((ab)^n = a^n b^n\). In this case, \(a = 4\) and \(b = x^3\):
\[
(4x^3)^2 = 4^2 (x^3)^2
\]
2. Now calculate \(4^2\) and \((x^3)^2\):
\[
4^2 = 16 \quad \text{and} \quad (x^3)^2 = x^{3 \cdot 2} = x^6
\]
3. Bringing everything together:
\[
(4x^3)^2 = 16x^6
\]
Now we have simplified \((4x^3)^2\) to \(16x^6\).
Regarding your question about whether the answer is \(8 \times 64 \times 6^6\) or \(16 \times 5\), the correct simplified expression is **neither**. The simplification of the original expression is \(16x^6\).