Horton Schneider
10/16/2023 · Primary School
1) Si \( a=-4 \quad b=2 \quad c=5 \quad d=7 \) Halla el valor numérico de a) \( 3 b^{4}+8 a c-9 d \) b) \( 3 c^{b}+6 a b d \)
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Tutor-Verified Answer
Step-by-step Solution
Para resolver las expresiones dadas, primero sustituimos los valores de \( a \), \( b \), \( c \) y \( d \):
- \( a = -4 \)
- \( b = 2 \)
- \( c = 5 \)
- \( d = 7 \)
Ahora, resolvemos cada parte:
a) \( 3 b^{4} + 8 a c - 9 d \)
Sustituyendo los valores:
\[
3 (2)^{4} + 8 (-4) (5) - 9 (7)
\]
Calculamos \( 2^{4} \):
\[
2^{4} = 16
\]
Ahora sustituimos:
\[
3 (16) + 8 (-4) (5) - 9 (7)
\]
Calculamos cada término:
\[
3 \cdot 16 = 48
\]
\[
8 \cdot (-4) \cdot 5 = -160
\]
\[
-9 \cdot 7 = -63
\]
Sumamos todos los términos:
\[
48 - 160 - 63
\]
Primero, sumamos \( 48 - 160 \):
\[
48 - 160 = -112
\]
Luego, sumamos \( -112 - 63 \):
\[
-112 - 63 = -175
\]
Por lo tanto, el valor de la expresión a) es:
\[
\boxed{-175}
\]
b) \( 3 c^{b} + 6 a b d \)
Sustituyendo los valores:
\[
3 (5)^{2} + 6 (-4) (2) (7)
\]
Calculamos \( 5^{2} \):
\[
5^{2} = 25
\]
Ahora sustituimos:
\[
3 (25) + 6 (-4) (2) (7)
\]
Calculamos cada término:
\[
3 \cdot 25 = 75
\]
\[
6 \cdot (-4) \cdot 2 \cdot 7 = -336
\]
Sumamos los términos:
\[
75 - 336
\]
Calculamos:
\[
75 - 336 = -261
\]
Por lo tanto, el valor de la expresión b) es:
\[
\boxed{-261}
\]
Quick Answer
a) \( 3 b^{4} + 8 a c - 9 d = -175 \)
b) \( 3 c^{b} + 6 a b d = -261 \)
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