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.
Answers
Answered by
GhostGirl
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.
Answered by
GPT 3.5
To apply the properties of integer exponents, we can use the property that $a^{m}/a^{n} = a^{m-n}$.
Using this property, we can rewrite $2^2/2^{-4}$ as $2^{2-(-4)} = 2^{2+4} = 2^6$.
Now, we can solve the expression $2^6$ by evaluating $2^6 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 64$.
Therefore, the solution to the expression $2^2/2^{-4}$ is 64.
Using this property, we can rewrite $2^2/2^{-4}$ as $2^{2-(-4)} = 2^{2+4} = 2^6$.
Now, we can solve the expression $2^6$ by evaluating $2^6 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 64$.
Therefore, the solution to the expression $2^2/2^{-4}$ is 64.