if x=8^2/3×32^-2/5, then x=x^-5
Answers
Answer:
Step-by-step explanation:
x
=
(
8
2
3
⋅
32
−
5
2
)
First, use this rule of exponents to rewrite each term on the right side:
x
a
×
b
=
(
x
a
)
b
x
=
(
8
2
×
1
3
⋅
32
−
5
×
1
2
)
x
=
(
(
8
2
)
1
3
⋅
(
32
−
5
)
1
2
)
Next, use this rule of exponents to rewrite the
32
term:
x
a
=
1
x
−
a
x
=
(
(
8
2
)
1
3
⋅
(
(
1
32
−
−
5
)
1
2
)
x
=
(
(
8
2
)
1
3
⋅
(
(
1
32
5
)
1
2
)
x
=
(
(
64
)
1
3
⋅
(
(
1
33554432
)
1
2
)
We can then use this rule to rewrite the exponents:
x
1
n
=
n
√
x
x
=
3
√
64
⋅
1
2
√
33554432
x
=
3
√
64
⋅
1
√
33554432
x
=
3
√
64
⋅
1
√
16777216
⋅
2
Now, use this rule to rewrite the denominator of the fraction:
√
a
⋅
b
=
√
a
⋅
√
b
x
=
3
√
64
⋅
1
√
16777216
⋅
2
x
=
4
⋅
1
√
16777216
√
2
x
=
4
⋅
1
4096
√
2
x
=
4
4096
√
2
x
=
1
1024
√
2
Next, we can rationalize the fraction:
x
=
√
2
√
2
⋅
1
1024
√
2
x
=
√
2
⋅
1
√
2
⋅
1024
√
2
x
=
√
2
1024
(
√
2
)
2
x
=
√
2
1024
⋅
2
x
=
√
2
2048
Or, approximately:
x
=
0.00069
Answer:
Step-by-step explanation:
x = 1
x = 1