How do you simplify $[(2x^-3 * y^-1) / (4x^-5 * y^-4)]^2 * [(8x^5 * y^6) / (4x^7 * y^4)]^3$ ?

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Answer 1 · 2017-10-11T10:29:42

$2x^-2y^12 or (2y^12)/x^2$

$[(2x^-3 cdot y^-1)/(4x^-5 cdot y^-4)]^2 cdot [(8x^5 cdot y^6)/(4x^7 cdot y^4)]^3$

Simplifying the coefficients first..

$[(cancel(2)^1x^-3 cdot y^-1)/(cancel(4)^2x^-5 cdot y^-4)]^2 cdot [(cancel(8)^2x^5 cdot y^6)/(cancel(4)^1x^7 cdot y^4)]^3$

$[(x^-3 cdot y^-1)/(2x^-5 cdot y^-4)]^2 cdot [(2x^5 cdot y^6)/(x^7 cdot y^4)]^3$

Using Indices..

Recall; $rArr x^a/x^b = x^(a - b)$

$[(1/2x^(-3 - (-5)) cdot y^(-1 - (-4)))]^2 cdot [(2x^(5 - 7) cdot y^(6 - 4))]^3$

Simplifying the indexes..

$[(1/2x^(-3 + 5) cdot y^(-1 + 4))]^2 cdot [(2x^-2 cdot y^2)]^3$

$[(1/2x^2 cdot y^3)]^2 cdot [(2x^-2 cdot y^2)]^3$

Multiplying the indexes to their respective brackets..

$((1/2)^2x^(2 xx 2) cdot y^(3 xx 2)) cdot 2^3x^(-2 xx 3) cdot y^(2 xx 3)$

$(1/4x^4 cdot y^6) cdot 8x^-6 cdot y^6$

$(1/cancel4_1x^4 cdot y^6) cdot cancel8^2x^-6 cdot y^6$

$x^4 cdot y^6 cdot 2x^-6 cdot y^6$

Using Indices..

Recall; $rArr x^a xx x^b = x^(a + b)$

$2x^(4 + (-6)) cdot y^(6 + 6)$

$2x^(4 - 6) cdot y^12$

$2x^-2y^12 or (2y^12)/x^2 -> Answer$

How do you simplify [(2x^-3 * y^-1) / (4x^-5 * y^-4)]^2 * [(8x^5 * y^6) / (4x^7 * y^4)]^3[(2x^-3 * y^-1) / (4x^-5 * y^-4)]^2 * [(8x^5 * y^6) / (4x^7 * y^4)]^3?