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Math Problems
Algebra 1
Simplify exponential expressions using exponent rules
Simplify. Express your answer using a single exponent.
\newline
(
w
6
)
−
8
(w^{6})^{-8}
(
w
6
)
−
8
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Simplify. Express your answer using positive exponents.
\newline
j
−
5
×
j
7
×
j
4
j^{-5} \times j^{7} \times j^{4}
j
−
5
×
j
7
×
j
4
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Simplify. Express your answer using a single exponent.
\newline
(
z
−
5
)
−
3
(z^{-5})^{-3}
(
z
−
5
)
−
3
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Write the expression as a fraction with a positive exponent.
\newline
1
w
6
\frac{1}{w^6}
w
6
1
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Simplify. Express your answer using a single exponent.
\newline
(
b
−
8
)
9
(b^{-8})^{9}
(
b
−
8
)
9
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Simplify. Express your answer using a single exponent.
\newline
(
j
9
)
−
9
(j^{9})^{-9}
(
j
9
)
−
9
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Write the expression as a variable with a negative exponent.
\newline
1
x
2
\frac{1}{x^2}
x
2
1
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Simplify. Express your answer using a single exponent.
\newline
(
t
2
)
3
(t^2)^3
(
t
2
)
3
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Simplify. Express your answer using a single exponent.
\newline
(
z
3
)
−
4
(z^{3})^{-4}
(
z
3
)
−
4
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Simplify. Express your answer using positive exponents.
\newline
r
−
2
r
−
7
⋅
r
8
\frac{r^{-2}}{r^{-7} \cdot r^{8}}
r
−
7
⋅
r
8
r
−
2
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Simplify. Express your answer using positive exponents.
\newline
a
−
2
×
a
5
×
a
−
5
a^{-2} \times a^{5} \times a^{-5}
a
−
2
×
a
5
×
a
−
5
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Simplify. Express your answer using a single exponent.
\newline
(
m
4
)
7
(m^{4})^{7}
(
m
4
)
7
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Simplify. Express your answer using a single exponent.
\newline
(
p
2
)
−
2
(p^2)^{-2}
(
p
2
)
−
2
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Simplify. Express your answer using a single exponent.
\newline
(
j
−
9
)
−
2
(j^{-9})^{-2}
(
j
−
9
)
−
2
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Simplify. Express your answer using a single exponent.
\newline
(
g
8
)
9
(g^{8})^{9}
(
g
8
)
9
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Write the expression as a variable with a negative exponent.
\newline
1
g
5
\frac{1}{g^5}
g
5
1
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Write the expression as a variable with a negative exponent.
\newline
1
m
5
\frac{1}{m^5}
m
5
1
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Simplify. Express your answer using positive exponents.
\newline
q
9
⋅
q
−
9
q
9
\frac{q^9 \cdot q^{-9}}{q^9}
q
9
q
9
⋅
q
−
9
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Write the expression as a variable with a negative exponent.
\newline
1
x
5
\frac{1}{x^5}
x
5
1
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Write the expression as a variable with a negative exponent.
\newline
1
j
6
\frac{1}{j^6}
j
6
1
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Simplify. Express your answer using a single exponent.
\newline
(
h
−
5
)
4
(h^{-5})^4
(
h
−
5
)
4
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Write the expression as a fraction with a positive exponent.
\newline
1
u
−
2
\frac{1}{u^{-2}}
u
−
2
1
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Simplify. Express your answer using a single exponent.
\newline
(
j
−
4
)
2
(j^{-4})^2
(
j
−
4
)
2
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Write the expression as a variable with a negative exponent.
\newline
1
z
8
\frac{1}{z^8}
z
8
1
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Write the expression as a variable with a negative exponent.
\newline
1
m
7
\frac{1}{m^7}
m
7
1
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Simplify. Express your answer using a single exponent.
\newline
(
q
7
)
6
(q^{7})^{6}
(
q
7
)
6
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Write the expression as a fraction with a positive exponent.
\newline
1
d
−
6
\frac{1}{d^{-6}}
d
−
6
1
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Write the expression as a fraction with a positive exponent.
\newline
1
u
7
\frac{1}{u^7}
u
7
1
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Write the expression as a variable with a negative exponent.
\newline
1
c
6
\frac{1}{c^6}
c
6
1
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Simplify. Express your answer using a single exponent.
\newline
(
h
3
)
−
7
(h^3)^{-7}
(
h
3
)
−
7
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Simplify. Express your answer using a single exponent.
\newline
(
z
6
)
−
4
(z^{6})^{-4}
(
z
6
)
−
4
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Simplify. Express your answer using a single exponent.
\newline
(
k
−
3
)
−
4
(k^{-3})^{-4}
(
k
−
3
)
−
4
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Simplify. Express your answer using positive exponents.
\newline
k
3
k
5
⋅
k
5
\frac{k^3}{k^5 \cdot k^5}
k
5
⋅
k
5
k
3
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Simplify. Express your answer using a single exponent.
\newline
(
j
−
7
)
5
(j^{-7})^5
(
j
−
7
)
5
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Simplify. Express your answer using positive exponents.
\newline
q
−
3
q
−
5
⋅
q
−
3
\frac{q^{-3}}{q^{-5} \cdot q^{-3}}
q
−
5
⋅
q
−
3
q
−
3
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Simplify. Express your answer using positive exponents.
\newline
q
7
q
6
⋅
q
−
2
\frac{q^7}{q^6 \cdot q^{-2}}
q
6
⋅
q
−
2
q
7
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Write the expression as a fraction with a positive exponent.
\newline
1
r
4
\frac{1}{r^{4}}
r
4
1
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Simplify. Express your answer using a single exponent.
\newline
(
x
−
7
)
−
8
(x^{-7})^{-8}
(
x
−
7
)
−
8
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Simplify. Express your answer using a single exponent.
\newline
(
x
−
5
)
−
9
(x^{-5})^{-9}
(
x
−
5
)
−
9
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Write the expression as a fraction with a positive exponent.
\newline
1
y
3
\frac{1}{y^3}
y
3
1
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Simplify. Express your answer using a single exponent.
\newline
(
r
8
)
5
(r^{8})^{5}
(
r
8
)
5
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Write the expression as a fraction with a positive exponent.
\newline
1
k
3
\frac{1}{k^3}
k
3
1
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Write the expression as a fraction with a positive exponent.
\newline
1
m
6
\frac{1}{m^6}
m
6
1
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Simplify. Express your answer using positive exponents.
\newline
w
−
3
w
−
3
\frac{w^{-3}} {w^{-3}}
w
−
3
w
−
3
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Determine the center and radius of the circle represented by the equation
\newline
(
x
−
17
)
2
+
(
y
−
19
)
2
=
49
(x-17)^2+(y-19)^2=49
(
x
−
17
)
2
+
(
y
−
19
)
2
=
49
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Write with a single exponent:
\newline
(
5
y
)
3
(5^{y})^{3}
(
5
y
)
3
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Evaluate the expression
10
(
3
)
x
10(3)^x
10
(
3
)
x
for
x
=
2
x=2
x
=
2
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The functions
\newline
f
(
x
)
=
5
(
2
)
x
f(x)=5(2)^{x}
f
(
x
)
=
5
(
2
)
x
and
\newline
g
(
x
)
=
5
(
b
)
x
g(x)=5(b)^{x}
g
(
x
)
=
5
(
b
)
x
are graphed in the
\newline
x
y
xy
x
y
-plane. If the graph of function
\newline
g
g
g
is always increasing and
\newline
f
(
x
)
>
g
(
x
)
f(x) > g(x)
f
(
x
)
>
g
(
x
)
for all
\newline
x
>
0
x > 0
x
>
0
, then which of the following could be the value of
\newline
b
b
b
?
\newline
Choose
1
1
1
answer:
\newline
(A)
0.25
0.25
0.25
\newline
(B)
1.25
1.25
1.25
\newline
(C)
2
2
2
\newline
(D)
g
(
x
)
=
5
(
b
)
x
g(x)=5(b)^{x}
g
(
x
)
=
5
(
b
)
x
0
0
0
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P
(
x
)
=
2
,
500
(
0.98
)
x
P(x)=2{,}500(0.98)^x
P
(
x
)
=
2
,
500
(
0.98
)
x
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Simplify. Express your answer using positive exponents.
\newline
h
−
2
h
−
8
\frac{h^{-2}}{h^{-8}}
h
−
8
h
−
2
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