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[tex](5xy^7)^2(y^2)^3=\\\\25x^2y^{14}*y^6=\\\\25x^2y^{20}[/tex]

The simplified form of the given expression is [tex]25 x^{2} y^{20}[/tex].

What is the simplified form of the expression?

Simplifying expressions mean rewriting the same algebraic expression with no like terms and in a compact manner.

What are the exponent rules?

The different Laws of exponents are:

  1. [tex]x^{m} .x^{n} =x^{m+n}[/tex]
  2. [tex]\frac{x^{m} }{x^{n} } = x^{m-n}[/tex]
  3. [tex](x^{m} )^{n} = x^{m\times n}[/tex]
  4. [tex]x^{0} =1[/tex]
  5. [tex]x^{-1} = \frac{1}{x}[/tex]

According to the given question.

We have an expression [tex](5xy^{7} )^{2}(y^{2} )^{3}[/tex]

To simplify the above expression we use the exponent rules.

Therefore,

[tex](5xy^{7} )^{2}(y^{2} )^{3}[/tex]

[tex]= 5^{2}x^{2} y^{7\times2} y^{2\times3}[/tex]

[tex]= 25 x^{2} y^{14} y^{6}[/tex]

[tex]= 25 x^{2} y^{14+6}[/tex]

[tex]= 25 x^{2} y^{20}[/tex]

Therefore, the simplified form of the given expression is [tex]25 x^{2} y^{20}[/tex] .

Find out the more information about the simplified form of the expression and exponent rules here:

https://brainly.com/question/14575743

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