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Simplify ((2a^-4b^-9c^-1)/(10a^-7bc^-5))^-1
(
2
a
-
4
b
-
9
c
-
1
10
a
-
7
b
c
-
5
)
-
1
Step 1
Move
b
-
9
to the
denominator
using the negative
exponent
rule
b
-
n
=
1
b
n
.
(
2
a
-
4
c
-
1
10
a
-
7
b
c
-
5
b
9
)
-
1
Step 2
Multiply
b
by
b
9
by adding the
exponents
.
Move
b
9
.
(
2
a
-
4
c
-
1
10
a
-
7
(
b
9
b
)
c
-
5
)
-
1
Multiply
b
9
by
b
.
Raise
b
to the
power
of
1
.
(
2
a
-
4
c
-
1
10
a
-
7
(
b
9
b
1
)
c
-
5
)
-
1
Use the
power rule
a
m
a
n
=
a
m
+
n
to
combine
exponents
.
(
2
a
-
4
c
-
1
10
a
-
7
b
9
+
1
c
-
5
)
-
1
(
2
a
-
4
c
-
1
10
a
-
7
b
9
+
1
c
-
5
)
-
1
Add
9
and
1
.
(
2
a
-
4
c
-
1
10
a
-
7
b
10
c
-
5
)
-
1
(
2
a
-
4
c
-
1
10
a
-
7
b
10
c
-
5
)
-
1
Step 3
Move
a
-
7
to the
numerator
using the negative
exponent
rule
1
b
-
n
=
b
n
.
(
2
a
-
4
c
-
1
a
7
10
b
10
c
-
5
)
-
1
Step 4
Move
c
-
5
to the
numerator
using the negative
exponent
rule
1
b
-
n
=
b
n
.
(
2
a
-
4
c
-
1
a
7
c
5
10
b
10
)
-
1
Step 5
Simplify the
numerator
.
Multiply
a
-
4
by
a
7
by adding the
exponents
.
Move
a
7
.
(
2
(
a
7
a
-
4
)
c
-
1
c
5
10
b
10
)
-
1
Use the
power rule
a
m
a
n
=
a
m
+
n
to
combine
exponents
.
(
2
a
7
-
4
c
-
1
c
5
10
b
10
)
-
1
Subtract
4
from
7
.
(
2
a
3
c
-
1
c
5
10
b
10
)
-
1
(
2
a
3
c
-
1
c
5
10
b
10
)
-
1
Multiply
c
-
1
by
c
5
by adding the
exponents
.
Move
c
5
.
(
2
a
3
(
c
5
c
-
1
)
10
b
10
)
-
1
Use the
power rule
a
m
a
n
=
a
m
+
n
to
combine
exponents
.
(
2
a
3
c
5
-
1
10
b
10
)
-
1
Subtract
1
from
5
.
(
2
a
3
c
4
10
b
10
)
-
1
(
2
a
3
c
4
10
b
10
)
-
1
(
2
a
3
c
4
10
b
10
)
-
1
Step 6
Cancel the
common factor
of
2
and
10
.
Factor
2
out of
2
a
3
c
4
.
(
2
(
a
3
c
4
)
10
b
10
)
-
1
Cancel the
common factors
.
Factor
2
out of
10
b
10
.
(
2
(
a
3
c
4
)
2
(
5
b
10
)
)
-
1
Cancel the
common factor
.
(
2
(
a
3
c
4
)
2
(
5
b
10
)
)
-
1
Rewrite the
expression
.
(
a
3
c
4
5
b
10
)
-
1
(
a
3
c
4
5
b
10
)
-
1
(
a
3
c
4
5
b
10
)
-
1
Step 7
Change the sign of the
exponent
by rewriting the
base
as its
reciprocal
.
5
b
10
a
3
c
4
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