Question
Simplify (x^2y^3)^-2(x^4)^2
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GPT 3.5
To simplify, we can apply the power rule, which states that when raising an exponent to another exponent, we multiply the exponents.
First, let's simplify the expression inside the parenthesis:
(x^2y^3)^-2 = x^(2*-2)y^(3*-2) = x^-4y^-6 = 1/(x^4y^6)
Now, let's simplify the expression outside the parenthesis:
(x^4)^2 = x^(4*2) = x^8
Putting it all together, the simplified expression is:
1/(x^4y^6) * x^8 = x^8 / (x^4y^6) = x^(8-4)y^-6 = x^4y^-6 or 1/(x^(-4)y^6)
First, let's simplify the expression inside the parenthesis:
(x^2y^3)^-2 = x^(2*-2)y^(3*-2) = x^-4y^-6 = 1/(x^4y^6)
Now, let's simplify the expression outside the parenthesis:
(x^4)^2 = x^(4*2) = x^8
Putting it all together, the simplified expression is:
1/(x^4y^6) * x^8 = x^8 / (x^4y^6) = x^(8-4)y^-6 = x^4y^-6 or 1/(x^(-4)y^6)
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