We are asked to simplify the expression `(4x^2y^3)^4 ` . (Note that we are not asked to solve since this is not an equation or inequality; simplifying produces an equivalent expression where solving produces solution(s).)
We will use the exponent rules:
(1) Use the power of a product rule: `(ab)^n=a^nb^n ` .
` (4x^2y^3)^4=4^4(x^2)^4(y^3)^4 ` ** The equals sign here indicates equivalent expressions, not an equation with solution(s). This will be true for any x,y in the domain.
(2) Now use the power of a power rule: `(a^m)^n=a^(m*n) `
So we have `4^4(x^2)^4(y^3)^4=256x^8y^12 `
This is simplified as there are no negative exponents and no parantheses.
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`(4x^2y^3)^4 ` is equivalent to (or simplifies as) `256x^8y^12 `
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