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Math Problems
Algebra 1
Simplify exponential expressions using exponent rules
f
(
t
)
=
1
,
000
(
1
16
)
t
4
f(t) = 1,000 \left(\frac{1}{16}\right)^{\frac{t}{4}}
f
(
t
)
=
1
,
000
(
16
1
)
4
t
which of the following is an equivalent form of the function
F
F
F
in which the base of the exponent is
1
2
\frac{1}{2}
2
1
?
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f
(
t
)
=
1
,
000
(
1
16
)
t
4
f(t) = 1,000 \left(\frac{1}{16}\right)^{\frac{t}{4}}
f
(
t
)
=
1
,
000
(
16
1
)
4
t
which of the following is an equivalent form of the function
f
f
f
in which the base of the exponent is
1
2
\frac{1}{2}
2
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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y
−
4
×
y
3
y^{-4} \times y^{3}
y
−
4
×
y
3
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y
−
4
⋅
y
3
y^{-4} \cdot y^{3}
y
−
4
⋅
y
3
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A monomial of the
2
2
2
nd degree with a leading coefficient of
3
3
3
. Choose
1
1
1
answer :
\newline
A.
3
n
2
−
1
3n^2-1
3
n
2
−
1
\newline
B.
3
n
−
2
3n^{-2}
3
n
−
2
\newline
C.
3
n
2
3n^2
3
n
2
\newline
D.
2
n
3
2n^3
2
n
3
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4
⋅
x
(
x
−
3
)
4 \cdot x(x-3)
4
⋅
x
(
x
−
3
)
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The functions
f
(
x
)
=
8
(
2
5
)
x
f(x)= 8\left(\frac{2}{5}\right)^x
f
(
x
)
=
8
(
5
2
)
x
and
g
(
x
)
=
8
(
b
)
x
g(x) = 8(b)^x
g
(
x
)
=
8
(
b
)
x
are graphed in the xy-plane. For what value of
b
b
b
would the graphs of functions
f
f
f
and
g
g
g
be symmetric with respect to the y-axis?
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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
(
m
−
3
)
4
(m^{-3})^{4}
(
m
−
3
)
4
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Write with a single exponent:
\newline
(
5
y
)
3
(5^{y})^{3}
(
5
y
)
3
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Write with a single exponent:
\newline
(
2
5
)
7
(2^{5})^{7}
(
2
5
)
7
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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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The graph of
y
=
12
(
0.25
)
x
y=12(0.25)^x
y
=
12
(
0.25
)
x
is shown in the
x
y
xy
x
y
-plane. Which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?
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Simplify. Express your answer using positive exponents.
\newline
r
9
⋅
r
8
⋅
r
-
5
r^9 \cdot r^8 \cdot r^{\text{-}5}
r
9
⋅
r
8
⋅
r
-
5
\newline
______
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