Which of the following is the equivalent expression to (15^−3 ⋅ 4^7)^0/4^−3 that has been generated by applying the Properties of Integer Exponents?(1 point)
1 ⋅ 4^-3
60/4^-3
64
1/64
1/64
Which of the following is an equivalent expression to (2^−3 ⋅ 9^3)^−4/2^9 ⋅9^−10 with only positive exponents, generated by applying the Properties of Integer Exponents?(1 point)
2^3 ⋅ 9^2
2^−7⋅ 9^−1/2^9⋅9^−10
2^3/9^2
2^12⋅9^−12/2^9⋅9^−10
2^3 ⋅ 9^2
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)
To generate an equivalent expression with only positive exponents:
3^7 ⋅ 3^−9 = 3^(7-9) = 3^(-2)
To convert this to a fraction with no remaining exponents:
3^(-2) = 1 / 3^2 = 1 / 9
Therefore, the equivalent expression with only positive exponents is 1 / 9.
Apply the Properties of Integer Exponents to generate equivalent expressions to 2^2/2^−4 with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point)
To generate an equivalent expression with only positive exponents:
2^2 / 2^(-4) = 2^(2 - (-4)) = 2^6
Solving the expression, we get:
2^6 = 64
Therefore, the solution is 64.
Apply the Properties of Integer Exponents to generate equivalent expressions to 4^0 ⋅ 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 generate equivalent expressions with only positive exponents:
4^0 ⋅ 5^−2/(−2)^−3
For 4^0, any non-zero number raised to the power of 0 is equal to 1, so 4^0 = 1.
Therefore, the expression becomes:
1 * 5^(-2) / (-2)^(-3)
To handle the negative exponents:
1 / 5^2 / (-2)^3 = 1 / (25 * (-8))
1 / (25 * (-8)) = -1/200
Therefore, the solution is -1/200.
bot this isn't right
I apologize for the errors in my previous responses. Let's correct this.
Given expression: 4^0 * 5^(-2) / (-2)^(-3)
First, simplify the exponents:
4^0 = 1
5^(-2) = 1/5^2 = 1/25
(-2)^(-3) = 1/(-2)^3 = 1/(-8)
Now, substitute the simplified exponents back into the expression:
1 * 1/25 / 1/(-8)
1/25 * (-8) = -8/25
Therefore, the simplified fraction with no remaining exponents is -8/25.