Question

simplify 5x squared y to the 4th (to the 3rd power)

Answer 1

To simplify \( (5x^2 y^4)^3 \), we apply the power of a product rule, which states that \( (ab)^n = a^n b^n \), and also the power of a power rule, which states that \( (a^m)^n = a^{mn} \).

1. Apply the power of the product:
\[
(5x^2 y^4)^3 = 5^3 (x^2)^3 (y^4)^3
\]

2. Calculate each part:
\[
5^3 = 125
\]
\[
(x^2)^3 = x^{2 \times 3} = x^6
\]
\[
(y^4)^3 = y^{4 \times 3} = y^{12}
\]

3. Combine all the parts:
\[
(5x^2 y^4)^3 = 125 x^6 y^{12}
\]

So, the simplified form is:
\[
\boxed{125 x^6 y^{12}}
\]