Simplify:

Question

left parenthesis, 5, x, to the power 4 , y, to the power 10 , right parenthesis, squared(5x
4
y
10
)
2

Answer
Attempt 1 out of 2
Multiple Choice Answers
10, x, to the power 8 , y, to the power 2010x
8
y
20

25, x, to the power 8 , y, to the power 2025x
8
y
20

10, x, to the power 6 , y, to the power 1210x
6
y
12

25, x, to the power 6 , y, to the power 1225x
6
y
12

Answer 1

To simplify \((5x^4y^{10})^2\):

1. Apply the power of a product rule, which states that \((ab)^n = a^n \cdot b^n\).

2. For the expression \((5)^2\), \( (x^4)^2\), and \( (y^{10})^2\):

   • \((5)^2 = 25\)
   • \((x^4)^2 = x^{4 \times 2} = x^8\)
   • \((y^{10})^2 = y^{10 \times 2} = y^{20}\)

Combining these results gives:

\[ (5x^4y^{10})^2 = 25x^8y^{20} \]

Looking at the multiple choice answers, the correct simplification is:

25, x, to the power 8, y, to the power 20.