Simplify. Express your answer using a single exponent.
(3t^7)²
____
Submit
Simplify. Express your answer using a single exponent. (3t^7)² Submit.
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Simplify. Express your answer using a single exponent.
(3t^7)²
____
Submit
To simplify ( (3t^7)^2 ), you can apply the power of a product rule and the power of a power rule.
1. Power of a product states that ( (ab)^n = a^n cdot b^n ). Here, ( 3 ) and ( t^7 ) are multiplied together, so we’ll apply the exponent to each.
[
(3t^7)^2 = 3^2 cdot (t^7)^2
]
2. Now calculate ( 3^2 ) and ( (t^7)^2 ):
[
3^2 = 9
]
[
(t^7)^2 = t^{7 cdot 2} = t^{14}
]
3. Combining these results gives:
[
(3t^7)^2 = 9t^{14}
]
So, the simplified expression is ( 9t^{14} ).