Question

Which is the simplified form of (StartFraction 2 a b Over a Superscript negative 5 Baseline b squared EndFraction) Superscript negative 3? Assume a not-equals 0, b not-equals 0. StartFraction b cubed Over 8 a Superscript 18 Baseline EndFraction StartFraction b squared Over 8 a Superscript 45 Baseline EndFraction StartFraction a Superscript 6 Baseline Over 4 b EndFraction StartFraction 2 a Superscript 6 Baseline Over b Superscript 5 Baseline EndFraction

Answer 1

A

Explanation:

just took the pretest! good luck!

Answer 2

`(b^3)/(8a^(18))` matches the first choice

Explanation:

`\left((2 a b)/(a^(-5)b^2)\right)^(-3)=(2a^(1-(-5))b^(1-2))^(-3)=(2a^6b^(-1))^(-3)\\\\=2^(-3)a^(6(-3))b^(-1(-3))=8^(-1)a^(-18)b^3=\boxed{(b^3)/(8a^(18))}`

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The applicable rules of exponents are ...

(a^b)(a^c) = a^(b+c)

(a^b)^c = a^(bc)

a^-b = 1/a^b