First, let's apply the properties of integer exponents to 40 ⋅ 5^(-2)(-2)^(-3):
1. Negative exponent property: a^(-n) = 1/a^n
40 ⋅ 5^(-2)(-2)^(-3) = 40/(5^2),(2^3)
= 40/(5^2)(2^3)
2. Product of powers property: a^n ⋅ a^m = a^(n+m)
40/(5^2)(2^3) = 40/((5^2)⋅(2^3))
Now, let's simplify the expression:
1. Calculate the exponent of each base:
(5^2) = 25
(2^3) = 8
2. Simplify the expression:
40/((5^2)⋅(2^3)) = 40/(25⋅8)
3. Calculate the value of 25⋅8:
25⋅8 = 200
4. Simplify the expression further:
40/200 = 1/5
Therefore, the simplified fraction with no remaining exponents is 1/5.
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)
3 answers
my apologies for the confusion
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)
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)
To apply the properties of integer exponents and generate equivalent expressions, we can rewrite the expression as follows:
40 ⋅ 5^(-2)(-2)^(-3)
Using the properties of exponents, we have:
1. Negative exponent property: a^(-n) = 1/a^n
Applying this property to 5^(-2), we get:
5^(-2) = 1/5^2
2. Negative exponent property: a^(-n) = 1/a^n
Applying this property to (-2)^(-3), we get:
(-2)^(-3) = 1/(-2)^3
Now, let's rewrite the expression using these equivalent forms:
40 ⋅ 5^(-2)(-2)^(-3) = 40 ⋅ (1/5^2) ⋅ (1/(-2)^3)
Next, we simplify the exponents:
1/5^2 = 1/25
1/(-2)^3 = 1/(-2 * -2 * -2) = 1/(-8) = -1/8
Now, substitute these simplified forms back into the expression:
40 ⋅ (1/5^2) ⋅ (1/(-2)^3) = 40 ⋅ (1/25) ⋅ (-1/8)
Next, multiply the numerators and denominators:
40 ⋅ (1/25) ⋅ (-1/8) = (40 ⋅ 1 ⋅ -1) / (25 ⋅ 8) = -40 / 200 = -1/5
Thus, the simplified fraction with no remaining exponents is -1/5.
40 ⋅ 5^(-2)(-2)^(-3)
Using the properties of exponents, we have:
1. Negative exponent property: a^(-n) = 1/a^n
Applying this property to 5^(-2), we get:
5^(-2) = 1/5^2
2. Negative exponent property: a^(-n) = 1/a^n
Applying this property to (-2)^(-3), we get:
(-2)^(-3) = 1/(-2)^3
Now, let's rewrite the expression using these equivalent forms:
40 ⋅ 5^(-2)(-2)^(-3) = 40 ⋅ (1/5^2) ⋅ (1/(-2)^3)
Next, we simplify the exponents:
1/5^2 = 1/25
1/(-2)^3 = 1/(-2 * -2 * -2) = 1/(-8) = -1/8
Now, substitute these simplified forms back into the expression:
40 ⋅ (1/5^2) ⋅ (1/(-2)^3) = 40 ⋅ (1/25) ⋅ (-1/8)
Next, multiply the numerators and denominators:
40 ⋅ (1/25) ⋅ (-1/8) = (40 ⋅ 1 ⋅ -1) / (25 ⋅ 8) = -40 / 200 = -1/5
Thus, the simplified fraction with no remaining exponents is -1/5.