Question 8: By what number should (−5)^{ −1} be multiplied so that the product is (−8) ^{−1}
Answer 8:
Let the number be x.
According to the question,
Question 9: By what number should (15) ^{−1} be multiplied so that the product may be equal to (−5)^{ −1} ?
Answer 9:
Let the required number be x.
Therefore,
x=−3
Hence, the required number is −3.
Question 10:
By what number should (−15)^{−1} be divided so that the quotient may be equal to (−5)−1?
Answer 10:
Expressing in fractional form, we get:
(−15)^{−1} = −1/15, > (a^{−1} = 1/a)
and
(−5)^{−1} = −1/5 > (a^{−1} = 1/a)
We have to find a number x such that
Solving this equation, we get: Hence, (−15)^{−1} should be divided by 1/3 to obtain (−5)^{−1}.
Question 11:
By what number should (5/3)^{−2} be multiplied so that the product may be (73)^{−1}?
Answer 11:
Expressing as a positive exponent, we have:
> (a−1 = 1/a) > ((a/b)n = (an)/(bn)) and(7/3)^{−1} = 3/7. > (a^{−1} = 1/a)
We have to find a number x such that
Multiplying both sides by 25/9, we get:Hence, (5/3)^{−2} should be multiplied by 25/21 to obtain (7/3)^{−1}.
Question 12:
Find x, ifQuestion 14: Find the value of x for which 5^{2x} ÷ 5^{−3} = 5^{5}.
Answer 14:
We have:
hence, x is 1.
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