# FRANK Solutions for Class 9 Maths Chapter 9 - Indices

Boost your logical thinking skills for scoring top marks by learning from our Frank Solutions for ICSE Class 9 Mathematics Chapter 9 Indices. Practise problems based on the laws of indices. The solutions for the chapter-based questions from the Frank textbook are created by our subject experts, and can be easily accessed on our online portal any time.

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## Chapter 9 - Indices Exercise Ex. 9.1

Solve for x:

3 x 7^{x} = 7 x 3^{x}

Solve for x:

2^{x + 3} + 2^{x + 1} = 320

Evaluate the following:

Evaluate the following:

Evaluate the following:

Write each of the following in the simplest form:

(a^{3})^{5} x a^{4}

Write each of the following in the simplest form:

a^{2} x a^{3} ÷ a^{4}

Write each of the following in the simplest form:

Write each of the following in the simplest form:

a^{-3 }x a^{2} x a^{0}

Write each of the following in the simplest form:

(b^{-2} - a^{-2}) ÷ (b^{-1} - a^{-1})

Simplify the following and express with positive index:

3p^{-2}q^{3} ÷ 2p^{3}q^{-2}

Simplify the following and express with positive index:

Simplify the following:

Simplify the following:

Simplify the following:

Simplify the following:

Simplify the following:

Simplify the following:

Simplify the following:

Simplify the following:

x^{m +2n}. x^{3m-8n}÷ x^{5m- 60}

Simplify the following:

Simplify the following:

Solve for x:

2^{2x + 1} = 8

Solve for x:

9 x 3^{x} = (27)^{2x - 5}

Solve for x:

2^{2x + 3} - 9 x 2^{x} + 1 = 0

Solve for x:

1 = p^{x}

Solve for x:

P^{3} x p^{-2} = p^{x}

Solve for x:

Solve for x:

Solve for x:

Solve for x:

2^{2x}^{- 1} -9 x 2^{x - 2} + 1= 0

Solve for x:

Solve for x:

Solve for x:

Solve for x:

9^{x + 4 }= 3^{2} x (27)^{x+1}

Find the value of (8p)^{p} if 9^{p + 2} - 9^{p}
= 240.

If a^{x} = b^{y} = c^{z} and abc =
1, show that

If 2250 = 2^{a}. 3^{b}. 5^{c}, find
a, b and c. Hence, calculate the value of 3^{a} x 2^{-b} x 5^{-c}.

Find the value of 'a' and 'b' if:

Find the value of 'a' and 'b' if:

Prove the following:

Prove the following:

Prove the following:

Prove the following:

Prove the following:

(x^{a})^{b-c} x (x^{b})^{c-a}
x (x^{c})^{a-b }= 1

Prove the following:

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