How do you simplify $(4x^5 (x^-1)^3)/(x^-2)^-2$ ?

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Answer 1 · 2016-06-16T10:21:41

$= 4/x^2$

Use the power law of indices.. "Multiply the indices".

$(4x^5(x^-3))/(x^4) " now simplify"$

$(4x^5 xx x^-3)/x^4 = (4x^2)/x^4$

$= 4/x^2$

OR, you could deal with the negative index first by moving it to the denominator so the index is positive.

$(4x^5)/(x^4 xx x^3) = (4x^5)/x^7$

$= 4/x^2$

Which method you use is entirely your choice, one is not better than the other.

Answer 2 · 2016-06-16T10:22:29

$(4x^5(x^(-1))^3)/(x^(-2))^(-2)=4/x^2$

We use the identities $(a^m)^n=a^(mxxn)$ , $a^mxxa^n=a^(m+n)$ and $a^m/a^n=a^(m-n)$

Hence, $(4x^5(x^(-1))^3)/(x^(-2))^(-2)$

= $(4x^5x^((-1)xx3))/(x^((-2)xx(-2))$

= $(4x^5x^(-3))/(x^4)$

= $4x^(5-3-4)$

= $4x^(-2)$

= $4/x^2$

How do you simplify (4x^5 (x^-1)^3)/(x^-2)^-2(4x^5 (x^-1)^3)/(x^-2)^-2?