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} ).