Question
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)
2^2/2^−4=
2^2/2^−4=
Answers
Answer
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)
Answer
Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3⋅27^−7)^0/3^4 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
Answered by
GPT 3.5
To generate an equivalent expression with only positive exponents, we can apply the property of exponents that states:
a^m / a^n = a^(m-n)
Using this property, we can rewrite the expression as:
2^2 / 2^(-4) = 2^(2-(-4)) = 2^6
Now, we can solve the expression.
2^6 = 2 * 2 * 2 * 2 * 2 * 2 = 64.
Therefore, the solution is 64 as a whole number.
a^m / a^n = a^(m-n)
Using this property, we can rewrite the expression as:
2^2 / 2^(-4) = 2^(2-(-4)) = 2^6
Now, we can solve the expression.
2^6 = 2 * 2 * 2 * 2 * 2 * 2 = 64.
Therefore, the solution is 64 as a whole number.
Answered by
GPT 3.5
To generate an equivalent expression with only positive exponents, we can apply the property of exponents that states:
a^0 = 1
Using this property, we can rewrite the expression as:
4^0 ⋅ 5^(-2) / (-2)^(-3) = 1 ⋅ (1/5^2) / (1/(-2)^3)
Now, let's simplify the expression:
1 ⋅ (1/5^2) / (1/(-2)^3) = (1/1) / (1/(8)) = 1 ⋅ (8/1) = 8
Therefore, the solution is 8.
a^0 = 1
Using this property, we can rewrite the expression as:
4^0 ⋅ 5^(-2) / (-2)^(-3) = 1 ⋅ (1/5^2) / (1/(-2)^3)
Now, let's simplify the expression:
1 ⋅ (1/5^2) / (1/(-2)^3) = (1/1) / (1/(8)) = 1 ⋅ (8/1) = 8
Therefore, the solution is 8.
Answered by
GPT 3.5
To generate an equivalent expression with only positive exponents, we can apply the property of exponents that states:
(a^m / b^n)^p = a^(m * p) / b^(n * p)
Applying this property, we can rewrite the expression as:
(14^3⋅27^−7)^0/3^4 = (14^(3*0) / 27^(−7*0)) / 3^(4*0) = (14^0 / 27^0) / 3^0
Recall that any term raised to the power of 0 is equal to 1. Therefore, we have:
(14^0 / 27^0) / 3^0 = (1/1) / 1 = 1/1 = 1
Therefore, the solution is 1.
(a^m / b^n)^p = a^(m * p) / b^(n * p)
Applying this property, we can rewrite the expression as:
(14^3⋅27^−7)^0/3^4 = (14^(3*0) / 27^(−7*0)) / 3^(4*0) = (14^0 / 27^0) / 3^0
Recall that any term raised to the power of 0 is equal to 1. Therefore, we have:
(14^0 / 27^0) / 3^0 = (1/1) / 1 = 1/1 = 1
Therefore, the solution is 1.