Question
epaso: \( 4(-3)+7(-5)+\sqrt{16 \cdot 25}+\sqrt[5]{4^{10}}-(-6)+9^{0} \)
Ask by Tyler Carlson. in Guatemala
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
El resultado es -4.
Solution
1. Calculamos \(4(-3)\):
\[
4(-3) = -12
\]
2. Calculamos \(7(-5)\):
\[
7(-5) = -35
\]
3. Calculamos \(\sqrt{16 \cdot 25}\):
Primero multiplicamos:
\[
16 \cdot 25 = 400
\]
Ahora la raíz cuadrada:
\[
\sqrt{400} = 20
\]
4. Calculamos \(\sqrt[5]{4^{10}}\):
Observamos que:
\[
4^{10} = (4^2)^5 = 16^5
\]
Entonces,
\[
\sqrt[5]{16^5} = 16
\]
5. Calculamos \(-(-6)\):
\[
-(-6) = 6
\]
6. Calculamos \(9^{0}\):
\[
9^{0} = 1
\]
7. Sumamos todos los términos:
\[
-12 + (-35) + 20 + 16 + 6 + 1
\]
Realizamos las operaciones paso a paso:
\[
-12 - 35 = -47
\]
\[
-47 + 20 = -27
\]
\[
-27 + 16 = -11
\]
\[
-11 + 6 = -5
\]
\[
-5 + 1 = -4
\]
El resultado final es:
\[
-4
\]
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Simplify this solution Bonus Knowledge
Let's break it down step by step! First, calculate \( 4(-3) = -12 \) and \( 7(-5) = -35 \). Their sum is \( -12 + (-35) = -47 \). Next, compute \( \sqrt{16 \cdot 25} = \sqrt{400} = 20 \). Then, for \( \sqrt[5]{4^{10}} \), we can rewrite it as \( (4^2)^{2} = 16^2 = 256 \) and \( \sqrt[5]{256} = 4 \) since \( 256 = 4^4 \), but staying with it in root form gives \( \sqrt[5]{2^{20}} = 2^4 = 16 \). Adding everything up: - Start with \( -47 + 20 + 16 \) gives \( -11 \). - Add \( 6 \) (the result of \(-(-6)\)) gives \( -5 \). - Finally, \( 9^{0} = 1 \). So the final result is \( -5 + 1 = -4 \). Therefore, the answer is \( -4 \).
