Question

Can someone help me on this please
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Answer 1

The answer is Option A

Explanation:

Start by dividing 54 by 6 which will give you 9

then divide b² by b^5 which will give you b³ at the denominator

then a^8÷a^-4

using indices...

=a^8-(-4)

=a^12

at the numerator

put everything together and you'll have...

9a^12/b³

Answer 2

A.
`\frac{9 \: {a}^(12) }{ {b}^(3) }` ✅

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`54 {a}^(8) {b}^(2) / 6 {a}^( - 4) {b}^(5)`

To solve the expression in a simpler way, single out the like terms.

Now, we have

`(54)/(6) . \frac{ {a}^(8) }{ {a}^( - 4) } . \frac{ {b}^(2) }{ {b}^(5) } \\ \\ = 9 \: {a}^(8 - ( - 4)) {b}^(2 - 5) \\ \\ (∵ \frac{ {a}^(m) }{ {a}^(n) } = {a}^(m - n) ) \\ \\ = 9 \: {a}^(8 + 4) {b}^( - 3) \\ \\ = 9 \: {a}^(12) {b}^( - 3) \\ \\ ( \: or \: ) \\ \\ = \frac{9 \: {a}^(12) }{ {b}^(3) } \\ \\ (∵ {a}^( - m) = \frac{1}{ {a}^(m) } )`

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