Question
simplify the expression
[(-1)^5/(-2)^-3]^2
[(-1)^5/(-2)^-3]^2
Answers
Answered by
GPT 3.5
To simplify the expression [(-1)^5/(-2)^-3]^2, we can start by simplifying the exponents separately.
First, let's start with (-1)^5. When we raise a negative number to an odd exponent, the result is always negative. So, (-1)^5 = -1.
Next, let's simplify (-2)^-3. When we raise a number to a negative exponent, we can rewrite it as the reciprocal of the number raised to the positive exponent. Therefore, (-2)^-3 = 1/(-2)^3.
Now, let's simplify the expression inside the square brackets: [-1/(1/(-2)^3)]^2 = [-1/(-8)]^2.
To simplify this further, we can simplify -1/(-8) by multiplying both the numerator and the denominator by -1: [(-1) * -1]/[(8) * -1] = 1/8.
Finally, we square this simplified expression: (1/8)^2 = 1/64.
Therefore, the simplified expression [(-1)^5/(-2)^-3]^2 is equal to 1/64.
First, let's start with (-1)^5. When we raise a negative number to an odd exponent, the result is always negative. So, (-1)^5 = -1.
Next, let's simplify (-2)^-3. When we raise a number to a negative exponent, we can rewrite it as the reciprocal of the number raised to the positive exponent. Therefore, (-2)^-3 = 1/(-2)^3.
Now, let's simplify the expression inside the square brackets: [-1/(1/(-2)^3)]^2 = [-1/(-8)]^2.
To simplify this further, we can simplify -1/(-8) by multiplying both the numerator and the denominator by -1: [(-1) * -1]/[(8) * -1] = 1/8.
Finally, we square this simplified expression: (1/8)^2 = 1/64.
Therefore, the simplified expression [(-1)^5/(-2)^-3]^2 is equal to 1/64.
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