PLease explain the simplification of: -x(x2)2

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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Supposing that you need to evaluate the expression `-x*(x^2)^2` , you need to respect the order of operations, hence you need to raise the term inside brackets to square and then you need to multiply by (-x) the result such that:

`(x^2)^2 = x^(2*2) = x^4`

Notice that you need to multiply the exponents such that: `(x^2)^2 = x^4.`

You need to multiply the result by -x, hence, you need to multiply the coefficients and the variables such that:

`(-x)*(x^4) = (-1)*(1)*(x*x^4) = - x^(1+4) = -x^5`

Notice that multiplication of two powers that have the same base means raising the base to the sum of exponents.

Hence, simplifying the given expression yields `(-x)*(x^2)^2 = -x^5.`

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