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

this is what were given\[ \Bigg(\frac{2ab}{a^{-5} b^2 } \Bigg) ^{-3 }\]we know that we can turn \(\frac{1}{b^{-n}}\) into \( b^n \) right? thats why we get \( a^6 \)-- then we just cancel the bs out \[ \Bigg(\frac{2a^6 \cancel{b}}{b^\cancel{2}}\Bigg)^{-3} \]

Answer 2

to turn the exponential \( {-3} \) into positive \(3\), we have to rewrite the fraction the way around, so that would be: \[ \Bigg(\frac{b}{2a^6 } \Bigg) ^3 \]

Answer 3

we just now should open the brackets:
\[ \frac{b^3}{2^3(a^6)^3 } \]

Answer 4

that gives us
\[ \frac{b^3}{8 \times a^{18} } \]

Answer 5

now that its fully simplified, which of the options is the right one?

Answer 6

https://media.edgenuity.com/evresources/3111-08-02/mc019-3.jpg

basically this?

Answer 7

yeah

Answer 8

So, uhh since you didn't react — which of the options is correct?

Answer 9

your answer