Apply the property of integer exponents to generate equivalent expression to 4^0.5^-2/(-2)^-3with only positive exponents then solve the expression. Your answer will be a simplified fraction with no remaining exponents
the question is written wrong, since exponents associate to the right. It should have been
(4^0.5)^-2/(-2)^-3
= 2^-2 * (-2)^3
= -2
Apologies for the misunderstanding. You are correct.
Taking into account the proper order of operations for exponentiation:
(4^0.5)^-2/(-2)^-3
= (2^-2) * (-2)^3
= (1/2^2) * (-8)
= (1/4) * (-8)
= -8/4
= -2
Therefore, the simplified fraction with no remaining exponents is -2.
To apply the property of integer exponents, remember that any number raised to the power of 0 is equal to 1. Also, when we have a negative exponent, we can rewrite it as the reciprocal of the base raised to the positive exponent.
Let's break down the given expression step by step:
1. Start with 4^(0.5^-2) / (-2)^-3
2. Rewrite 0.5^-2 as (1/0.5)^2 since a negative exponent turns the number into its reciprocal: 4^(1/0.5)^2 / (-2)^-3
3. Simplify the expression inside the parentheses: 4^(2/1)^2 / (-2)^-3
4. Apply the property of integer exponents to 4^(2/1)^2:
- Since the exponent is a fraction, take the square root of the base (4) first: √4 = 2
- Then raise 2 to the power of the numerator (2): 2^2 = 4
So, 4^(2/1)^2 becomes 4^2 = 16.
5. Apply the property of integer exponents to (-2)^-3:
- Since the exponent is negative, take the reciprocal of the base: 1/(-2)
- Then raise the reciprocal (1/(-2)) to the power of the absolute value of the exponent (3): (1/(-2))^3 = 1/(-8) = -1/8.
Now, let's simplify the expression after applying the property of integer exponents:
16 / (-1/8)
To divide by a fraction, we multiply by its reciprocal:
16 * (-8/1)
Multiply the numerator and the denominator:
-128/1
The simplified fraction with no remaining exponents is -128/1, which is just -128. So, the final answer is -128.
To apply the property of integer exponents, we can rewrite the expression as follows:
4^0.5^-2/(-2)^-3
= (1/4^2)/(-1/2)^3
Now, let's simplify this expression:
= (1/16)/(-1/8)
= 1/16 * -8/-1
= -8/16
= -1/2
Therefore, the simplified fraction with no remaining exponents is -1/2.