Apply the Properties of Integer Exponents to generate an equivalent expression to 80⋅ 435−2
with only positive exponents, then solve the expression. (1 point)
To generate an equivalent expression with only positive exponents, we can use the property of negative exponents:
a^(-n) = 1/(a^n)
Applying this property to the given expression (80 * 435^(-2)), we can rewrite it as:
80 / (435^2)
Now we can solve the expression:
80 / (435^2) = 80 / (435 * 435) = 80 / 189,225
To simplify further, we can divide 80 by 189,225:
80 / 189,225 ≈ 0.0004221879679738925
To generate an equivalent expression with only positive exponents, we can apply the properties of integer exponents.
The property we can apply is: a^(-b) = 1 / (a^b).
Using this property, we can rewrite the expression 435^(-2) as 1 / 435^2.
Now we can rewrite the given expression 80 * (1 / 435^2).
To solve the expression, we can first simplify 1 / 435^2.
435^2 = 435 * 435 = 189,225
Therefore, 1 / 435^2 = 1 / 189,225.
Now we can substitute this value back into the expression: 80 * (1 / 189,225).
Multiplying 80 by 1 gives us: 80 / 189,225.
Therefore, the equivalent expression with only positive exponents is: 80 / 189,225.
To apply the properties of integer exponents and generate an equivalent expression with only positive exponents, we can use the following rules:
1. Product Rule: a^m * a^n = a^(m+n)
2. Quotient Rule: a^m / a^n = a^(m-n)
3. Power of a Power Rule: (a^m)^n = a^(m*n)
4. Power of a Product Rule: (a * b)^n = a^n * b^n
Now let's apply these rules to the given expression:
80 * 435^(-2)
First, we can rewrite 435^(-2) using the Quotient Rule as 1 / 435^(2).
So, the expression becomes:
80 * (1 / 435^(2))
Next, we can rewrite 1 / 435^(2) as 435^(-2) using the Power of a Power Rule.
Therefore, the expression simplifies to:
80 * 435^(-2)
Now, let's calculate the value of the expression:
80 * 435^(-2) = 80 * (1 / 435^(2))
To simplify further, we can calculate the value of 435^2:
435^2 = 435 * 435 = 189,225
Now, substituting this value back into the expression:
80 * (1 / 189,225) = 80 / 189,225
So, the expression is simplified to 80 / 189,225.