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Let’s check out your problem:
(
x
3
y
5
)
3
⋅
−
x
6
y
5
\left(x^{3} y^{5}\right)^{3} \cdot-x^{6} y^{5}
(
x
3
y
5
)
3
⋅
−
x
6
y
5
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Math Problems
Calculus
Find derivatives of using multiple formulae
Full solution
Q.
(
x
3
y
5
)
3
⋅
−
x
6
y
5
\left(x^{3} y^{5}\right)^{3} \cdot-x^{6} y^{5}
(
x
3
y
5
)
3
⋅
−
x
6
y
5
Simplify and Apply Power Rule:
Simplify the expression inside the parentheses and apply the power rule
(
a
m
)
n
=
a
m
∗
n
(a^m)^n = a^{m*n}
(
a
m
)
n
=
a
m
∗
n
.
\newline
(
x
3
y
5
)
3
=
x
3
∗
3
y
5
∗
3
=
x
9
y
15
(x^{3}y^{5})^{3} = x^{3*3}y^{5*3} = x^9y^{15}
(
x
3
y
5
)
3
=
x
3
∗
3
y
5
∗
3
=
x
9
y
15
Multiply Simplified Expression:
Multiply the simplified expression by the remaining terms.
x
9
y
15
×
−
x
6
y
5
=
−
x
(
9
+
6
)
y
(
15
+
5
)
=
−
x
15
y
20
x^9y^{15} \times -x^6y^5 = -x^{(9+6)}y^{(15+5)} = -x^{15}y^{20}
x
9
y
15
×
−
x
6
y
5
=
−
x
(
9
+
6
)
y
(
15
+
5
)
=
−
x
15
y
20
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