To simplify the expression [tex]\(\left(x^{10} - 5y^2\right)^3\)[/tex], you can follow these steps:
Step 1: Identify the given expression.
The given expression is [tex]\(\left(x^{10} - 5y^2\right)^3\)[/tex].
Step 2: Check if the expression can be factored further.
In this case, the expression inside the parentheses, [tex]\(x^{10} - 5y^2\)[/tex], does not have common factors and does not fit a recognizable factorization pattern such as difference of squares or cubes.
Step 3: Recognize that raising a polynomial to a power and ensuring it stays in its simplified form may not generally result in further factorization unless higher-level factorization techniques are applied.
Step 4: Write down the simplified expression.
Since there is no further simplification possible without expanding the expression (which is typically not done unless explicitly required), the simplified form of the expression remains:
[tex]\[
(x^{10} - 5y^2)^3
\][/tex]
Step 5: Conclude with the final simplified expression.
The final simplified expression is:
[tex]\[
(x^{10} - 5y^2)^3
\][/tex]
Therefore, the simplified form of [tex]\(\left(x^{10} - 5y^2\right)^3\)[/tex] is [tex]\((x^{10} - 5y^2)^3\)[/tex].
