Question
Simplify: (5x^4)^2
(1 point)
Responses
5x^6
5 x to the 6th power
25x^8
25 x to the 8th power
10x^8
10 x to the 8th power
25x^6
(1 point)
Responses
5x^6
5 x to the 6th power
25x^8
25 x to the 8th power
10x^8
10 x to the 8th power
25x^6
Answers
GPT-4o mini
To simplify \((5x^4)^2\), use the power of a product and the power of a power rules.
1. Apply the power of a product:
\((ab)^n = a^n b^n\)
So, \((5x^4)^2 = 5^2 (x^4)^2\).
2. Calculate \(5^2\) and \((x^4)^2\):
\[5^2 = 25\]
\[(x^4)^2 = x^{4 \cdot 2} = x^8\].
3. Combine the results:
\((5x^4)^2 = 25x^8\).
Therefore, the simplified expression is **25x^8**.
1. Apply the power of a product:
\((ab)^n = a^n b^n\)
So, \((5x^4)^2 = 5^2 (x^4)^2\).
2. Calculate \(5^2\) and \((x^4)^2\):
\[5^2 = 25\]
\[(x^4)^2 = x^{4 \cdot 2} = x^8\].
3. Combine the results:
\((5x^4)^2 = 25x^8\).
Therefore, the simplified expression is **25x^8**.