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**Question 8: ****By what number should (âˆ’5) ^{ âˆ’1} be multiplied so that the product is (âˆ’8) ^{âˆ’1}**

**Answer 8:**

Let the number be x.

According to the question,

**Question 9: By what number should (15) ^{âˆ’1} be multiplied so that the product may be equal to (âˆ’5)^{ âˆ’1} ?**

**Answer 9****:**

Let the required number be x.

Therefore,

x=âˆ’3

Hence, the required number is âˆ’3. **Question 10:**

**By what number should (âˆ’15) ^{âˆ’1} be divided so that the quotient may be equal to (âˆ’5)âˆ’1?**

**Answer 10:**

Expressing in fractional form, we get:

(âˆ’15)^{âˆ’1} = âˆ’1/15, ---> (a^{âˆ’1} = 1/a)

and

(âˆ’5)^{âˆ’1} = âˆ’1/5 ---> (a^{âˆ’1} = 1/a)

We have to find a number x such that

Solving this equation, we get: Hence, (âˆ’15)^{âˆ’1} should be divided by 1/3 to obtain (âˆ’5)^{âˆ’1}.

**Question 11:**

**By what number should (5/3) ^{âˆ’2} be multiplied so that the product may be (73)^{âˆ’1}?**

**Answer 11:**

Expressing as a positive exponent, we have:

---> (aâˆ’1 = 1/a) ---> ((a/b)n = (an)/(bn)) and(7/3)^{âˆ’1} = 3/7. ---> (a^{âˆ’1} = 1/a)

We have to find a number x such that

Multiplying both sides by 25/9, we get:Hence, (5/3)^{âˆ’2} should be multiplied by 25/21 to obtain (7/3)^{âˆ’1}.

**Question 12:**

(a

x = 3

(a

x = 6

x = 1/2

x = 10/3

x = 322Ã—23-4 = Hence,

(ii) First, we have to find

Hence, the value of

**Question 14: Find the value of x for which **5^{2x} Ã· 5^{âˆ’3} = 5^{5}.**Answer 14:****We have:**

hence, x is 1.