Simplify. Express your answer using a single exponent.
(10t⁷)²
A) 10²t¹⁴
B) 10⁷t²
C) 10¹⁴t²
D) 10²t⁷
Simplify. Express your answer using a single exponent. (10t⁷)²
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To simplify ((10t^{7})^{2}), you apply the power of a product rule, which states ((ab)^{n} = a^{n}b^{n}).
1. Apply the exponent to both the 10 and (t^7):
[
(10)^{2} cdot (t^{7})^{2}
]
2. Simplify each part:
[
10^{2} cdot t^{14}
]
So, the final simplified expression is (10^{2}t^{14}).
The correct answer is A) (10^{2}t^{14}).