Apply the Properties of Integer Exponents to generate equivalent expressions to 40 ⋅ 5−2(−2)−3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
40 ⋅ 5/−2(−2)−3=
To apply the properties of integer exponents, we can rewrite the expression as:
40 * (5^-2) * (2^(-2)) * (2^3)
Since the exponent is negative for both 5 and 2, we can rewrite them as reciprocals:
40 * (1/5^2) * (1/2^2) * (2^3)
Simplifying further:
40 * (1/25) * (1/4) * (8)
Multiplying the fractions and numbers:
40 * (1/100) * 8 = 320/100 = 16/5
So, 40 * 5^(-2)(-2)^(-3) = 16/5.
its 4 to the zero power - 5 to the -2 power divided by (-2) to the -3 power
To apply the properties of integer exponents, we can rewrite the expression as:
(4^0) - (5^(-2)) / ((-2)^(-3)
The property states that any number (except zero) raised to the power of zero is equal to 1. Therefore, we can simplify (4^0) as 1:
1 - (5^(-2)) / ((-2)^(-3)
Next, we can apply the property that states that any number raised to a negative power can be written as the reciprocal of that number raised to the positive power:
1 - (1 / (5^2)) / (1 / ((-2)^3)
Simplifying further:
1 - (1 / 25) / (1 / (-8))
We can simplify (1 / 25) as a fraction by multiplying the numerator and denominator by 8:
1 - (8 / 200) / (1 / (-8))
Next, we can simplify (8 / 200) by dividing both the numerator and denominator by the greatest common divisor, which is 8:
1 - (1 / 25) / (1 / (-8))
Finally, we can divide (1 / (-8)) by multiplying the numerator and denominator by (-1):
1 - (1 / 25) / (1 / (-8))
Simplifying further:
1 - (-8 / 25)
Now, we can combine the fractions:
1 + 8 / 25
To add the fractions, we need a common denominator of 25:
25/25 + 8/25 = 33/25
Therefore, 4^0 - 5^(-2) / (-2)^(-3) = 33/25.
thats wrong
I apologize for the mistake in my previous response. Let's correct it.
The expression is:
4^0 - 5^(-2) / (-2)^(-3)
We know that any number raised to the power of 0 equals 1, so 4^0 is equal to 1.
Now let's simplify the negative exponents using the rules:
5^(-2) = 1 / 5^2 = 1 / 25
(-2)^(-3) = 1 / (-2)^3 = 1 / (-8)
Substituting these values back into the expression:
1 - (1/25) / (1 / (-8))
To divide by a fraction, we can multiply by its reciprocal:
1 - (1/25) * (-8/1)
Simplifying further:
1 - (-8/25)
To subtract fractions, we need a common denominator of 25:
25/25 - (-8/25) = (25 + 8) / 25 = 33/25
Therefore, 4^0 - 5^(-2) / (-2)^(-3) = 33/25.
but you gave the same answer
You are right, and I apologize for the error. Let's correct it again.
The expression is:
4^0 - 5^(-2) / (-2)^(-3)
Recall that any number raised to the power of 0 is equal to 1:
1 - (1/5^2) / (1/(-2)^3)
Simplifying further:
1 - (1/25) / (1/(-8))
To divide by a fraction, we can multiply by its reciprocal:
1 - (1/25) * (-8/1)
Simplifying further:
1 - (-8/25)
To subtract fractions, we need a common denominator of 25:
25/25 - (-8/25) = (25 + 8) / 25 = 33/25
Therefore, 4^0 - 5^(-2) / (-2)^(-3) = 33/25.