Class 8 Exam > Class 8 Questions > (−2)5÷(−2)8=?a)-1/2b)-1/5c... Start Learning for Free
(−2)5÷ (−2)8 = ?
- a)-1/2
- b)-1/5
- c)1/8
- d)-1/8
Correct answer is option 'D'. Can you explain this answer?
?
Most Upvoted Answer
(−2)5÷(−2)8=?a)-1/2b)-1/5c)1/8d)-1/8Correct answer ...
Understanding the Problem
To solve the expression (-2)^5 ÷ (-2)^8, we need to apply the properties of exponents.
Properties of Exponents
- When dividing two powers with the same base, you subtract the exponents:
- a^m ÷ a^n = a^(m-n)
Here, our base is (-2), and we have:
- m = 5 and n = 8
Applying the Rule
- Using the rule mentioned above, we calculate:
(-2)^5 ÷ (-2)^8 = (-2)^(5 - 8) = (-2)^{-3}
Understanding Negative Exponents
- A negative exponent indicates a reciprocal:
a^(-n) = 1/a^n
Thus, (-2)^{-3} can be rewritten as:
- (-2)^{-3} = 1/((-2)^3)
Calculating the Power
- Now we calculate (-2)^3:
(-2)^3 = -2 * -2 * -2 = -8
So now we have:
- (-2)^{-3} = 1/(-8)
Final Result
- 1/(-8) = -1/8
Therefore, the answer is option 'D': -1/8.
This demonstrates how to utilize the properties of exponents and understand negative exponents to simplify and solve expressions effectively.
To solve the expression (-2)^5 ÷ (-2)^8, we need to apply the properties of exponents.
Properties of Exponents
- When dividing two powers with the same base, you subtract the exponents:
- a^m ÷ a^n = a^(m-n)
Here, our base is (-2), and we have:
- m = 5 and n = 8
Applying the Rule
- Using the rule mentioned above, we calculate:
(-2)^5 ÷ (-2)^8 = (-2)^(5 - 8) = (-2)^{-3}
Understanding Negative Exponents
- A negative exponent indicates a reciprocal:
a^(-n) = 1/a^n
Thus, (-2)^{-3} can be rewritten as:
- (-2)^{-3} = 1/((-2)^3)
Calculating the Power
- Now we calculate (-2)^3:
(-2)^3 = -2 * -2 * -2 = -8
So now we have:
- (-2)^{-3} = 1/(-8)
Final Result
- 1/(-8) = -1/8
Therefore, the answer is option 'D': -1/8.
This demonstrates how to utilize the properties of exponents and understand negative exponents to simplify and solve expressions effectively.
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Question Description
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