Apply the Properties of Integer Exponents to generate equivalent expressions to 3^7⋅3^−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents (1 point)
3^7⋅3^−9=
Using the property of integer exponents, we can add the exponents when multiplying with the same base.
Therefore, 3^7⋅3^−9 can be rewritten as 3^(7 + (-9)).
Simplifying the exponent, 7 + (-9) = -2.
So, 3^7⋅3^−9 is equivalent to 3^(-2).
To solve the expression, we know that any number raised to the power of -1 is equal to its reciprocal, so 3^(-1) is equal to 1/3.
Therefore, 3^(-2) is equal to 1/(3^2).
Simplifying further, 3^2 = 3*3 = 9.
Therefore, 3^(-2) is equal to 1/9.
So, the final answer is 1/9.
Using the property of integer exponents, we can subtract the exponents when dividing with the same base.
Therefore, 2^2/2^(-4) can be rewritten as 2^(2 - (-4)).
Simplifying the exponent, 2 - (-4) = 2 + 4 = 6.
So, 2^2/2^(-4) is equivalent to 2^6.
To solve the expression, 2^6 is equal to 2 * 2 * 2 * 2 * 2 * 2.
Simplifying further, 2^6 = 64.
Therefore, the solution to 2^2/2^(-4) is 64, a whole number.
Apply the Properties of Integer Exponents to generate equivalent expressions to 222−4 with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point)
2^2/2^−4=
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 generate equivalent expressions with positive exponents, let's simplify the expression step by step using the properties of integer exponents.
First, we can simplify the negative exponent by taking the reciprocal of the base. So, 5^(-2) is equivalent to 1/(5^2).
Next, let's simplify the exponent inside the parentheses by using the property of negative exponents. 2^(-2) is equivalent to 1/(2^2).
So, 5^(-2) and 2^(-2) can be replaced with the fractions 1/(5^2) and 1/(2^2), respectively.
Now, we have 40 ⋅ (1/(5^2)) ⋅ (1/(2^2)) ⋅ (-3).
To simplify further, we can multiply the fractions: 1/(5^2) ⋅ 1/(2^2) = 1/(25*4).
Therefore, the expression becomes 40 ⋅ (1/(25*4)) ⋅ (-3).
Multiplying the fractions and the -3: 40 ⋅ (1/(25*4)) ⋅ (-3) = (40*(-3))/(25*4) = -120/(100) = -6/5.
So, the solution to the expression 40 ⋅ 5^(-2) ⋅ 2^(-2) ⋅ (-3) is -6/5.
That is wrong
I apologize for the mistake. Let's go through the problem again.
The expression is 40 ⋅ 5^(-2(−2))(-3).
To simplify the expression, we can start by simplifying the exponent inside the parentheses:
-2(−2) = -2 * (-2) = 4
So the expression becomes 40 ⋅ 5^4 ⋅ (-3).
Next, we use the property of integer exponents to simplify 5^4:
5^4 = (5^2)^2 = (25)^2 = 625
Now the expression is 40 ⋅ 625 ⋅ (-3).
We can multiply 40 and 625 to get:
40 ⋅ 625 = 25,000
So the expression simplifies to:
25,000 ⋅ (-3).
Multiplying 25,000 and -3, we get:
25,000 ⋅ (-3) = -75,000.
Therefore, the solution to the expression 40 ⋅ 5^(-2(−2))(-3) is -75,000.