### Question 16

### 7 comments

###### Oluwasegun Solaja

1 year ago

@Goodness Barak thank you for this.

You got it.

Thanks for providing step by step explanation.

###### Dura Johnson

1 year ago

@goodness barak showed more workings and step by step process. I think he should take it

###### Goodness Barak

1 year ago

Expanding....

[(2³ m^9) / (r^6 n-¹²)] ÷ [(5² m-⁴ n^-6) / r² ]

Moving on...... Division can now change to multiplication for the numerator and denominator to swap position...

[(8m^9) / (r^6 n-¹²)] × [(r²)/(25m-⁴n^-6)]

r² will now cancel out r² out of r^6 we now have...

[(8m^9) / (r⁴ n^-12)] × [ (1) /(25 m-⁴n^-6)]

Multiplying...

[8m^9] /[ 25r⁴ m-⁴ n^-12 n^-6)

Since n^-12 and n^-6 has the same base we'll pick one and add the powers making it n^-12+(-6) = n^-18 using the law of indices.

We now have...

[8m^9] / [25 r^4 m^-4 n^-18]

Grouping them using brackets.. We have

(8/25)(m^9 / m^-4)(1/r^4)(1/n^-18)

Using the law of indices for m^9 and m^-4 = m^9-(-4) = m^13

(8/25)(m^13)(1/r^4)(1/n^-18)

Opening back the brackets

[8m^13] / [25r^4 n^-18]

This can be the simplified form but it can also be written as

[8m^13 r^-4 n^18] / 25.