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Math Problems
Algebra 1
Evaluate integers raised to rational exponents
80
100
\frac{80}{100}
100
80
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Perform the operation and express your answer as a single fraction in simplest form.
\newline
1
−
3
4
x
3
1-\frac{3}{4 x^{3}}
1
−
4
x
3
3
\newline
Answer:
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What is the conjugate of
−
4
7
−
8
7
i
-\frac{4}{7}-\frac{8}{7} i
−
7
4
−
7
8
i
?
\newline
−
4
7
+
8
7
i
-\frac{4}{7}+\frac{8}{7} i
−
7
4
+
7
8
i
\newline
4
7
−
8
7
i
\frac{4}{7}-\frac{8}{7} i
7
4
−
7
8
i
\newline
4
7
+
8
7
i
\frac{4}{7}+\frac{8}{7} i
7
4
+
7
8
i
\newline
−
8
7
−
4
7
i
-\frac{8}{7}-\frac{4}{7} i
−
7
8
−
7
4
i
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Simplify.
1
2
+
1
6
−
(
−
3
)
\frac{1}{2}+\frac{1}{6}-(-3)
2
1
+
6
1
−
(
−
3
)
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sin
−
1
(
−
1
)
\sin ^{-1}(-1)
sin
−
1
(
−
1
)
=
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Expand the expression : (a)
(
x
2
−
2
)
(
x
2
+
6
)
\left(x^{2}-2\right)\left(x^{2}+6\right)
(
x
2
−
2
)
(
x
2
+
6
)
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Evaluate the following expression.
\newline
−
112
7
+
9
-\frac{112}{7+9}
−
7
+
9
112
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Factor each completely.
\newline
6
x
2
+
28
x
+
16
6x^{2}+28x+16
6
x
2
+
28
x
+
16
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Rewrite using a positive exponent.
\newline
n
−
5
n^{-5}
n
−
5
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Simplify
(
3
y
3
)
4
{(3y^{3})^{4}}
(
3
y
3
)
4
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Find factors of the quadratic expression:
6
x
2
−
3
x
−
9
6x^{2}-3x-9
6
x
2
−
3
x
−
9
\newline
(
?
x
+
?
)
(
x
+
?
)
(?x+?)(x+?)
(
?
x
+
?)
(
x
+
?)
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Find factors of the quadratic expression:
3
v
2
−
6
v
+
3
3v^{2}-6v+3
3
v
2
−
6
v
+
3
\newline
(
?
v
+
?
)
(
v
+
?
)
(?v+?)(v+?)
(
?
v
+
?)
(
v
+
?)
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Integrate the function
8
x
−
5
x
2
+
6
x
3
\frac{8}{x}-\frac{5}{x^{2}}+\frac{6}{x^{3}}
x
8
−
x
2
5
+
x
3
6
with respect to
x
x
x
.
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Simplify:
\newline
(
−
4
p
)
(
−
6
p
4
)
(-4 p)\left(-6 p^{4}\right)
(
−
4
p
)
(
−
6
p
4
)
\newline
Answer:
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Simplify:
\newline
(
5
p
4
)
(
5
p
)
\left(5 p^{4}\right)(5 p)
(
5
p
4
)
(
5
p
)
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
32
x
10
y
5
)
−
1
5
\left(32 x^{10} y^{5}\right)^{-\frac{1}{5}}
(
32
x
10
y
5
)
−
5
1
\newline
Answer:
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Simplify the following expression to simplest form using only positive exponents.
\newline
(
49
x
2
y
8
)
−
1
2
\left(49 x^{2} y^{8}\right)^{-\frac{1}{2}}
(
49
x
2
y
8
)
−
2
1
\newline
Answer:
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ii)
1
3
(
2
3
−
1
3
)
\frac{1}{\sqrt{3}}\left(2 \sqrt{3}-\frac{1}{\sqrt{3}}\right)
3
1
(
2
3
−
3
1
)
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\newline
Find the value of
x
2
+
1
x
2
x^{2}+\frac{1}{x^{2}}
x
2
+
x
2
1
when
x
+
1
x
=
2
3
x+\frac{1}{x}=\frac{2}{3}
x
+
x
1
=
3
2
,
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y
=
−
2
2
y
+
3
y=\frac{-2}{2 y+3}
y
=
2
y
+
3
−
2
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∫
tan
−
1
(
5
x
)
d
x
\int \tan ^{-1}(5 x) d x
∫
tan
−
1
(
5
x
)
d
x
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lim
x
→
0
(
sin
(
x
)
x
)
\lim _{x \rightarrow 0}\left(\frac{\sin (x)}{x}\right)
lim
x
→
0
(
x
s
i
n
(
x
)
)
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Evaluate:
10
−
4
(
5
6
)
10-4\left(\frac{5}{6}\right)
10
−
4
(
6
5
)
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−
9
x
3
+
72
x
5
-9 x^{3}+72 x^{5}
−
9
x
3
+
72
x
5
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x
5
+
2
=
x
3
\frac{x}{5}+2=\frac{x}{3}
5
x
+
2
=
3
x
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tan
−
1
(
1
8
x
+
9
)
\tan ^{-1}\left(\frac{1}{8 x+9}\right)
tan
−
1
(
8
x
+
9
1
)
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Solve the differential equation
d
y
d
x
=
3
x
y
2
\frac{d y}{d x}=\frac{3}{x y^{2}}
d
x
d
y
=
x
y
2
3
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Simplify
(
x
2
−
5
x
+
7
)
−
(
3
x
2
−
4
x
+
2
)
\left(x^{2}-5 x+7\right)-\left(3 x^{2}-4 x+2\right)
(
x
2
−
5
x
+
7
)
−
(
3
x
2
−
4
x
+
2
)
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Fully simplify using only positive exponents.
\newline
30
x
6
y
7
50
x
6
y
6
\frac{30 x^{6} y^{7}}{50 x^{6} y^{6}}
50
x
6
y
6
30
x
6
y
7
\newline
Answer:
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Multiply.
\newline
10
x
(
−
5
x
2
+
8
)
10 x\left(-5 x^{2}+8\right)
10
x
(
−
5
x
2
+
8
)
\newline
Answer:
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Factor the expression completely.
\newline
x
4
+
4
x
2
+
3
x^{4}+4 x^{2}+3
x
4
+
4
x
2
+
3
\newline
Answer:
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Factor the expression completely.
\newline
x
4
+
7
x
3
x^{4}+7 x^{3}
x
4
+
7
x
3
\newline
Answer:
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Factor the expression completely.
\newline
−
24
−
20
x
4
-24-20 x^{4}
−
24
−
20
x
4
\newline
Answer:
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Factor the expression completely.
\newline
70
x
−
40
x
4
70 x-40 x^{4}
70
x
−
40
x
4
\newline
Answer:
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Factor the expression completely.
\newline
−
16
−
36
x
4
-16-36 x^{4}
−
16
−
36
x
4
\newline
Answer:
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2
x
y
+
4
x
y
−
1
2
x
y
2 x y+4 x y-\frac{1}{2} x y
2
x
y
+
4
x
y
−
2
1
x
y
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For which values of
x
x
x
is the expression undefined?
\newline
8
x
+
64
x
2
−
4
x
−
12
\frac{8x+64}{x^{2}-4x-12}
x
2
−
4
x
−
12
8
x
+
64
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Write the given expression as an algebraic expression in
x
x
x
.
\newline
tan
(
2
cos
−
1
(
x
)
)
\tan(2\cos^{-1}(x))
tan
(
2
cos
−
1
(
x
))
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Which value of
x
x
x
satisfies the equation
4
5
(
x
−
1
4
)
=
−
21
5
\frac{4}{5}\left(x-\frac{1}{4}\right)=-\frac{21}{5}
5
4
(
x
−
4
1
)
=
−
5
21
?
\newline
5
5
5
\newline
6
6
6
\newline
−
6
-6
−
6
\newline
−
5
-5
−
5
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Which value of
x
x
x
satisfies the equation
3
5
(
x
−
1
3
)
=
−
13
5
\frac{3}{5}\left(x-\frac{1}{3}\right)=-\frac{13}{5}
5
3
(
x
−
3
1
)
=
−
5
13
?
\newline
5
5
5
\newline
4
4
4
\newline
−
5
-5
−
5
\newline
−
4
-4
−
4
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Which value of
x
x
x
satisfies the equation
3
4
(
x
−
1
5
)
=
−
69
10
\frac{3}{4}\left(x-\frac{1}{5}\right)=-\frac{69}{10}
4
3
(
x
−
5
1
)
=
−
10
69
?
\newline
9
9
9
\newline
10
10
10
\newline
−
10
-10
−
10
\newline
−
9
-9
−
9
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Which value of
x
x
x
satisfies the equation
1
5
(
x
−
2
5
)
=
−
17
25
\frac{1}{5}\left(x-\frac{2}{5}\right)=-\frac{17}{25}
5
1
(
x
−
5
2
)
=
−
25
17
?
\newline
3
3
3
\newline
−
4
-4
−
4
\newline
−
3
-3
−
3
\newline
4
4
4
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Which expression has the same value as
1
−
2
1-2
1
−
2
?
\newline
−
2
+
1
-2+1
−
2
+
1
\newline
−
2
+
(
−
1
)
-2+(-1)
−
2
+
(
−
1
)
\newline
−
1
+
(
−
2
)
-1+(-2)
−
1
+
(
−
2
)
\newline
1
−
(
−
2
)
1-(-2)
1
−
(
−
2
)
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Which expression has the same value as
9
+
(
−
5
)
9+(-5)
9
+
(
−
5
)
?
\newline
5
−
9
5-9
5
−
9
\newline
−
9
+
(
−
5
)
-9+(-5)
−
9
+
(
−
5
)
\newline
−
5
−
9
-5-9
−
5
−
9
\newline
9
−
5
9-5
9
−
5
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Which expression is equivalent to
−
5
+
(
−
9
)
-5+(-9)
−
5
+
(
−
9
)
?
\newline
−
9
+
5
-9+5
−
9
+
5
\newline
9
−
(
−
5
)
9-(-5)
9
−
(
−
5
)
\newline
−
5
−
(
−
9
)
-5-(-9)
−
5
−
(
−
9
)
\newline
−
5
−
9
-5-9
−
5
−
9
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Which expression has the same value as
3
−
(
−
10
)
3-(-10)
3
−
(
−
10
)
?
\newline
3
+
10
3+10
3
+
10
\newline
10
+
(
−
3
)
10+(-3)
10
+
(
−
3
)
\newline
3
−
10
3-10
3
−
10
\newline
10
−
3
10-3
10
−
3
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Rewrite the expression in the form
\newline
a
n
a^{n}
a
n
.
\newline
a
5
a
(
5
2
)
=
□
−
x
\frac{a^{5}}{a^{\left(\frac{5}{2}\right)}}=\square^{-x}
a
(
2
5
)
a
5
=
□
−
x
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simplity.
\newline
cos
3
(
x
)
+
sin
2
(
x
)
cos
(
x
)
\cos^3(x)+\sin^2(x)\cos(x)
cos
3
(
x
)
+
sin
2
(
x
)
cos
(
x
)
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Differentiate
y
−
(
2
x
+
1
)
5
(
x
3
−
x
+
1
)
4
y-(2x+1)^{5}(x^{3}-x+1)^{4}
y
−
(
2
x
+
1
)
5
(
x
3
−
x
+
1
)
4
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Differentiate
y
=
(
2
x
+
1
)
5
(
x
3
−
x
+
1
)
4
y=(2x+1)^{5}(x^{3}-x+1)^{4}
y
=
(
2
x
+
1
)
5
(
x
3
−
x
+
1
)
4
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