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Math Problems
Algebra 1
Simplify radical expressions with variables
Find the root. Assume that all variables represent nonnegative real numbers.
\newline
256
x
32
4
\sqrt[4]{256 x^{32}}
4
256
x
32
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Find the root. Assume that all variables represent nonnegative real numbers.
\newline
4096
x
42
6
\sqrt[6]{4096 x^{42}}
6
4096
x
42
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If
f
(
x
)
=
−
2
x
+
7
f(x) = -2x + 7
f
(
x
)
=
−
2
x
+
7
, what is the value of
f
(
3
)
f(3)
f
(
3
)
?
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Let
a
a
a
be a non-zero rational number. Is
a
a
a
times the square root of
8
8
8
rational or irrational?
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Let
a
a
a
be a non-zero rational number. Is
a
a
a
times the square root of
8
8
8
rational or irrational?
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4
sin
(
x
)
d
x
4\sin(x)\,dx
4
sin
(
x
)
d
x
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Simplify. Remove all perfect squares from inside the square root. Assume
a
a
a
is positive.
108
a
6
\sqrt{108a^6}
108
a
6
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Consider the expression
4
(
8
x
+
5
)
4(8 x+5)
4
(
8
x
+
5
)
.
\newline
Complete
2
2
2
descriptions of the parts of the expression.
\newline
1
1
1
. The entire expression is the product of
\newline
2
2
2
. On its own,
(
8
x
+
5
)
(8 x+5)
(
8
x
+
5
)
is a sum with
□
\square
□
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Simplify.
\newline
Remove all perfect squares from inside the square root. Assume
x
x
x
is positive.
\newline
54
x
7
=
□
\sqrt{54 x^{7}}= \square
54
x
7
=
□
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Simplify. Assume
f
f
f
is greater than or equal to zero.
\newline
18
f
8
\sqrt{18f^8}
18
f
8
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Simplify. Assume
j
j
j
is greater than or equal to zero.
\newline
8
j
8
\sqrt{8j^8}
8
j
8
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Simplify. Assume
x
x
x
is greater than or equal to zero.
\newline
45
x
9
\sqrt{45x^9}
45
x
9
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Simplify. Assume
x
x
x
is greater than or equal to zero.
\newline
75
x
9
\sqrt{75x^9}
75
x
9
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Simplify. Assume
n
n
n
is greater than or equal to zero.
\newline
75
n
7
\sqrt{75n^7}
75
n
7
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Simplify. Assume
b
b
b
is greater than or equal to zero.
\newline
75
b
10
\sqrt{75b^{10}}
75
b
10
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Simplify. Assume
b
b
b
is greater than or equal to zero.
\newline
75
b
3
\sqrt{75b^3}
75
b
3
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Simplify. Assume
f
f
f
is greater than or equal to zero.
\newline
75
f
9
\sqrt{75f^9}
75
f
9
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Simplify. Assume
y
y
y
is greater than or equal to zero.
\newline
75
y
7
\sqrt{75y^7}
75
y
7
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Simplify. Assume
m
m
m
is greater than or equal to zero.
\newline
20
m
9
\sqrt{20m^9}
20
m
9
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Simplify. Assume
x
x
x
is greater than or equal to zero.
\newline
45
x
5
\sqrt{45x^5}
45
x
5
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Simplify. Assume
q
q
q
is greater than or equal to zero.
\newline
8
q
2
\sqrt{8q^2}
8
q
2
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Simplify. Assume
q
q
q
is greater than or equal to zero.
\newline
12
q
10
\sqrt{12q^{10}}
12
q
10
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Simplify. Assume
a
a
a
is greater than or equal to zero.
\newline
18
a
4
\sqrt{18a^4}
18
a
4
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Simplify. Assume
x
x
x
is greater than or equal to zero.
\newline
20
x
3
\sqrt{20x^3}
20
x
3
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Simplify. Assume
s
s
s
is greater than or equal to zero.
\newline
45
s
3
\sqrt{45s^3}
45
s
3
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Simplify. Assume
q
q
q
is greater than or equal to zero.
\newline
50
q
9
\sqrt{50q^9}
50
q
9
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Simplify. Assume
q
q
q
is greater than or equal to zero.
\newline
18
q
4
\sqrt{18q^4}
18
q
4
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Simplify. Assume
g
g
g
is greater than or equal to zero.
\newline
50
g
\sqrt{50g}
50
g
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Simplify to a single trig function with no denominator.
\newline
tan
θ
⋅
cot
2
θ
\tan \theta \cdot \cot ^{2} \theta
tan
θ
⋅
cot
2
θ
\newline
Answer:
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Simplify to a single trig function with no denominator.
\newline
cos
θ
⋅
tan
θ
\cos \theta \cdot \tan \theta
cos
θ
⋅
tan
θ
\newline
Answer:
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Simplify to a single trig function with no denominator.
\newline
sin
θ
⋅
csc
θ
\sin \theta \cdot \csc \theta
sin
θ
⋅
csc
θ
\newline
Answer:
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Find the argument of the complex number
9
−
3
3
i
9-3 \sqrt{3} i
9
−
3
3
i
in the interval
0
≤
θ
<
2
π
0 \leq \theta<2 \pi
0
≤
θ
<
2
π
.
\newline
Express your answer in terms of
π
\pi
π
.
\newline
Answer:
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Find the argument of the complex number
−
2
2
+
2
2
i
-2 \sqrt{2}+2 \sqrt{2} i
−
2
2
+
2
2
i
in the interval
0
≤
θ
<
2
π
0 \leq \theta<2 \pi
0
≤
θ
<
2
π
. Express your answer in terms of
π
\pi
π
.
\newline
Answer:
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Find the argument of the complex number
6
−
2
3
i
6-2 \sqrt{3} i
6
−
2
3
i
in the interval
0
≤
θ
<
2
π
0 \leq \theta<2 \pi
0
≤
θ
<
2
π
.
\newline
Express your answer in terms of
π
\pi
π
.
\newline
Answer:
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Find the argument of the complex number
4
−
4
i
4-4 i
4
−
4
i
in the interval
0
≤
θ
<
2
π
0 \leq \theta<2 \pi
0
≤
θ
<
2
π
.
\newline
Express your answer in terms of
π
\pi
π
.
\newline
Answer:
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Simplify.
\newline
Remove all perfect squares from inside the square root. Assume
x
x
x
is positive.
\newline
20
x
8
=
\sqrt{20 x^{8}}=
20
x
8
=
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Simplify.
\newline
Remove all perfect squares from inside the square roots. Assume
a
a
a
and
b
b
b
are positive.
\newline
42
a
4
b
6
=
□
\sqrt{42 a^{4} b^{6}}=\square
42
a
4
b
6
=
□
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Given
g
(
x
)
=
4
x
−
2
g(x)=4 x-2
g
(
x
)
=
4
x
−
2
, find
g
(
6
)
g(6)
g
(
6
)
.
\newline
Answer:
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Assuming
x
x
x
and
y
y
y
are both positive, write the following expression in simplest radical form.
\newline
18
x
7
y
2
\sqrt{18 x^{7} y^{2}}
18
x
7
y
2
\newline
Answer:
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Assuming
x
x
x
and
y
y
y
are both positive, write the following expression in simplest radical form.
\newline
25
x
4
y
7
\sqrt{25 x^{4} y^{7}}
25
x
4
y
7
\newline
Answer:
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Write the following expression without negative exponents and without parentheses.
\newline
4
x
−
1
4 x^{-1}
4
x
−
1
\newline
Answer:
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Translate the statement into an equation. Let x repr
37
37
37
is
7
7
7
less than double a number.
\newline
The given statement can be represented mathematic: (Do not simplify.)
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Evaluate the expression
(
−
4
+
1
i
)
−
(
2
+
7
i
)
(-4+1 i)-(2+7 i)
(
−
4
+
1
i
)
−
(
2
+
7
i
)
and write the result in the form
a
+
b
i
a+b i
a
+
bi
.
\newline
The real number
a
a
a
equals
_
_
_
_
_
\_\_\_\_\_
_____
\newline
The real number
b
b
b
equals
_
_
_
_
_
\_\_\_\_\_
_____
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Simplify.
\newline
Remove all perfect squares from inside the square root. Assume
\newline
a
a
a
is positive.
\newline
108
a
6
\sqrt{108a^{6}}
108
a
6
=
□
\square
□
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A function is invertible if it is
\newline
a) surjective
\newline
b) bijective
\newline
c) injective
\newline
d) neither surjective nor injective
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Write the expression
ln
2
+
4
\ln 2+4
ln
2
+
4
as a single logarithm in simplest form without any negative exponents.
\newline
Answer:
ln
(
□
)
\ln (\square)
ln
(
□
)
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
200
=
\sqrt{200}=
200
=
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
98
\sqrt{98}
98
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
45
\sqrt{45}
45
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Simplify.
\newline
Remove all perfect squares from inside the square root.
\newline
125
\sqrt{125}
125
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