See the attachment and Plz help me to find the answer
Answers
Question:
By what number should (-3/2)^-3 be divided so that quotient may be (-8/27)^-2.
Answer:
8³/27³
Step-by-step explanation:
Given that (-3/2)^-3 is divided by a number to get the quotient (-8/27)^-2. We need to find out the number.
Assumption: Let's say that (-3/2)^-3 is divided by x to get the quotient (-8/27)^-2.
→ (-3/2)-³ ÷ x = (-8/27)-²
→ (-3/2)-³ = (-8/27)-² × x
→ (-3/2)-³ × (27/-8)-² = x
Now, 3³ can be written as 27 and 2³ as 8 So,
→ (27/8)-¹ × (27/8)-² = x
We know that reciprocal of any number is it's power in negative. Similarly, if we do the reciprocal of the number whose power is negative then it will be positive one. So,
→ (8/27)¹ × (8/27)² = x
Law of exponents:
- a^m × a^n = a^(m + n)
- a^m/a^n = a^(m - n)
- a^0 = 1
- a^-1 = 1/a
- (a^m)^n = a^(m × n)
From above we can write 8/27 × (8/27)² as 8^(1 + 2)/27^(1 + 2)
→ 8^(1 + 2)/27^(1 + 2)
→ 8³/27³
Therefore, (-3/2)^-3 should be divided by 8³/27³ so that quotient may be (-8/27)^-2.
Question:
By what number should (-3/2)^-3 be divided so that quotient may be (-8/27)^-2.
Answer:
8³/27³
Step-by-step explanation:
Given that (-3/2)^-3 is divided by a number to get the quotient (-8/27)^-2. We need to find out the number.
Assumption: Let's say that (-3/2)^-3 is divided by x to get the quotient (-8/27)^-2.
→ (-3/2)-³ ÷ x = (-8/27)-²
→ (-3/2)-³ = (-8/27)-² × x
→ (-3/2)-³ × (27/-8)-² = x
Now, 3³ can be written as 27 and 2³ as 8 So,
→ (27/8)-¹ × (27/8)-² = x
We know that reciprocal of any number is it's power in negative. Similarly, if we do the reciprocal of the number whose power is negative then it will be positive one. So,
→ (8/27)¹ × (8/27)² = x
Law of exponents:
a^m × a^n = a^(m + n)
a^m/a^n = a^(m - n)
a^0 = 1
a^-1 = 1/a
(a^m)^n = a^(m × n)
From above we can write 8/27 × (8/27)² as 8^(1 + 2)/27^(1 + 2)
→ 8^(1 + 2)/27^(1 + 2)
→ 8³/27³
Therefore, (-3/2)^-3 should be divided by 8³/27³ so that quotient may be (-8/27)^-2.
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