Selina solutions
Our top 5% students will be awarded a special scholarship to Lido.

Chapter 7- Indices [exponents] | Exercise 7(C)

Question 8

\frac{9^{n} \cdot 3^{2} \cdot 3^{n}-(27)^{n}}{\left(3^{m} \cdot 2\right)^{3}}=3^{-3}

If

Show that: m-n=1

Looking to do well in your science exam ?  
Learn from an expert tutor. Book a free class!

\begin{array}{l} \frac{9^{n} \cdot 3^{2} \cdot 3^{n}-(27)^{n}}{\left(3^{m} \cdot 2\right)^{3}}=3^{-3} \\ \Rightarrow \frac{3^{2 n} \cdot 3^{2} \cdot 3^{n}-3^{3 n}}{3^{3 m} \cdot 2^{3}}=\frac{1}{3^{3}} \\ \Rightarrow \frac{3^{3 n} \cdot 3^{2}-3^{3 n}}{3^{3 m} \cdot 2^{3}}=\frac{1}{3^{3}} \\ \Rightarrow \frac{3^{3 n}\left(3^{2}-1\right)}{3^{3 m} \times 8}=\frac{1}{3^{3}} \\ \Rightarrow \frac{3^{3 n} \times 8}{3^{3 n} \times 8}=\frac{1}{3^{3}} \\ \Rightarrow \frac{1}{3^{3(m-n)}}=\frac{1}{3^{3 \times 1}} \\ \Rightarrow m-n=1 \quad \text { (proved) } \end{array}

Set your child up for success with Lido, book a class today!

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta

Question 8

\frac{9^{n} \cdot 3^{2} \cdot 3^{n}-(27)^{n}}{\left(3^{m} \cdot 2\right)^{3}}=3^{-3}

If

Show that: m-n=1

Looking to do well in your science exam ? Learn from an expert tutor. Book a free class!

\begin{array}{l} \frac{9^{n} \cdot 3^{2} \cdot 3^{n}-(27)^{n}}{\left(3^{m} \cdot 2\right)^{3}}=3^{-3} \\ \Rightarrow \frac{3^{2 n} \cdot 3^{2} \cdot 3^{n}-3^{3 n}}{3^{3 m} \cdot 2^{3}}=\frac{1}{3^{3}} \\ \Rightarrow \frac{3^{3 n} \cdot 3^{2}-3^{3 n}}{3^{3 m} \cdot 2^{3}}=\frac{1}{3^{3}} \\ \Rightarrow \frac{3^{3 n}\left(3^{2}-1\right)}{3^{3 m} \times 8}=\frac{1}{3^{3}} \\ \Rightarrow \frac{3^{3 n} \times 8}{3^{3 n} \times 8}=\frac{1}{3^{3}} \\ \Rightarrow \frac{1}{3^{3(m-n)}}=\frac{1}{3^{3 \times 1}} \\ \Rightarrow m-n=1 \quad \text { (proved) } \end{array}

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
Connect with us on social media!
2021 © Quality Tutorials Pvt Ltd All rights reserved
`