Simplify. Express your answer using exponents. (12c²d⁷)² Submit it should end only with words

To simplify the expression ( (12c^2d^7)^2 ), you will apply the power of a product rule and the power of a power rule for exponents.

1. Use the power of a product rule: When you have a product raised to a power, you can distribute the exponent to each factor inside the parentheses.

[

(ab)^n = a^n cdot b^n

]

So, for our expression:

[

(12c^2d^7)^2 = 12^2 cdot (c^2)^2 cdot (d^7)^2

]

2. Calculate each part:

– ( 12^2 = 144 )

– ( (c^2)^2 = c^{2 cdot 2} = c^4 )

– ( (d^7)^2 = d^{7 cdot 2} = d^{14} )

3. Combine all parts together:

[

144c^4d^{14}

]

So, the simplified expression is ( 144c^4d^{14} ).

If you have any more questions or need further assistance, feel free to ask!