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Math Problems
Grade 7
Powers with negative bases
-
2
5
2^5
2
5
=
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If
2
10
×
2
15
2^{10} \times 2^{15}
2
10
×
2
15
is expressed as some integer to the fifth power, what is that integer?
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8
+
8
1
4
=
8+\frac{8}{1^{4}}=
8
+
1
4
8
=
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Estimate. Which sign makes the statement true?
\newline
44
,
162
÷
384
44,162 \div 384
44
,
162
÷
384
?
?
?
987
987
987
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
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Estimate. Which sign makes the statement true?
\newline
329
÷
26
329 \div 26
329
÷
26
?
?
?
96
96
96
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
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Estimate. Which sign makes the statement true?
\newline
757
÷
76
757 \div 76
757
÷
76
?
?
?
2
2
2
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
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Estimate. Which sign makes the statement true?
\newline
902
÷
71
902 \div 71
902
÷
71
?
?
?
89
89
89
\newline
Choices:
\newline
(A)
>
>
>
\newline
(B)
<
<
<
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Solve for
x
x
x
:
7
−
x
2
=
6
7-x^2 = 6
7
−
x
2
=
6
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Solve for
x
x
x
. Your answer must be simplified.
−
3
-3
−
3
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Evaluate:
(
4
0
+
4
−
1
)
×
2
2
(4^{0} + 4^{-1}) \times 2^{2}
(
4
0
+
4
−
1
)
×
2
2
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Evaluate.
\newline
(
−
4
)
2
=
(-4)^2 =
(
−
4
)
2
=
_____
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Evaluate. Write your answer as a whole number or as a simplified fraction.
\newline
6
7
6
4
=
\frac{6^{7}}{6^{4}}=
6
4
6
7
=
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Evaluate.
\newline
3
2
−
3
5
=
2
□
32^{\frac{-3}{5}}=2^{\square}
3
2
5
−
3
=
2
□
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(
3
m
n
)
4
(3 m n)^{4}
(
3
mn
)
4
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ii)
(
−
10
)
+
3
=
(-10)+3=
(
−
10
)
+
3
=
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(
k
6
)
5
\left(k^{6}\right)^{5}
(
k
6
)
5
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6
2
÷
3
(
2
)
+
6
6^2\div3(2)+6
6
2
÷
3
(
2
)
+
6
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(
5
−
3
)
3
(\sqrt{5}-3)^3
(
5
−
3
)
3
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24
3
1
5
=
243^{\frac{1}{5}}=
24
3
5
1
=
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Evaluate. Write your answer as a whole number or as a simplified fraction.
\newline
4
8
4
4
=
\frac{4^{8}}{4^{4}}=
4
4
4
8
=
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(
8
x
2
)
2
3
=
\left(8 x^{2}\right)^{\frac{2}{3}}=
(
8
x
2
)
3
2
=
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What is the square root of
5
5
5
to the power of
4
3
?
\frac{4}{3}?
3
4
?
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Simplify the expression:
(
1
+
2
)
2
(1+2)^2
(
1
+
2
)
2
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(
3
2
+
9
)
×
(
[
1
+
9
]
×
2
)
=
(3^{2}+9)\times([1+9]\times2)=
(
3
2
+
9
)
×
([
1
+
9
]
×
2
)
=
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−
4
\sqrt{-4}
−
4
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Find the positive solution of the equation.
\newline
5
x
7
5
−
27
=
10485733
5 x^{\frac{7}{5}}-27=10485733
5
x
5
7
−
27
=
10485733
\newline
Answer:
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Find the positive solution of the equation.
\newline
5
x
6
5
+
11
=
2657216
5 x^{\frac{6}{5}}+11=2657216
5
x
5
6
+
11
=
2657216
\newline
Answer:
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5
×
(
a
+
b
+
c
)
=
5\times(a+b+c)=
5
×
(
a
+
b
+
c
)
=
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What is the value of
log
1
\log 1
lo
g
1
?
\newline
Answer:
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Simplify. Your answer should be in proper scientific notation:
\newline
Double
7
×
1
0
5
7 \times 10^{5}
7
×
1
0
5
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Solve for all values of
x
x
x
.
\newline
9
x
=
x
9
\frac{9}{x}=\frac{x}{9}
x
9
=
9
x
\newline
Answer:
x
=
x=
x
=
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Solve for all values of
x
x
x
.
\newline
x
10
=
5
2
x
\frac{x}{10}=\frac{5}{2 x}
10
x
=
2
x
5
\newline
Answer:
x
=
x=
x
=
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Write the following expression without negative exponents and without parentheses.
\newline
(
3
x
)
−
3
(3 x)^{-3}
(
3
x
)
−
3
\newline
Answer:
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Factor
27
n
3
+
64
27 n^{3}+64
27
n
3
+
64
completely.
\newline
Answer:
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Factor
d
3
−
1
d^{3}-1
d
3
−
1
completely.
\newline
Answer:
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Find each difference.
\newline
6
−
3
=
6-3=
6
−
3
=
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Evaluate. Write your answer as a whole number or as a simplified fraction.
\newline
1
0
5
1
0
3
=
\frac{10^{5}}{10^{3}}=
1
0
3
1
0
5
=
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3
−
4
3-4
3
−
4
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Evaluate. Write your answer as a whole number or as a simplified fraction.
\newline
3
5
3
3
=
\frac{3^{5}}{3^{3}}=
3
3
3
5
=
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Evaluate. Write your answer as a whole number or as a simplified fraction.
\newline
3
9
3
5
=
□
\frac {3^{9}}{3^{5}}=\square
3
5
3
9
=
□
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Subtract.
\newline
3
10
−
9
10
=
\frac{3}{10}-\frac{9}{10}=
10
3
−
10
9
=
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Solve for
x
\mathrm{x}
x
in simplest form.
\newline
13
=
1
2
(
x
−
2
)
13=\frac{1}{2}(x-2)
13
=
2
1
(
x
−
2
)
\newline
Answer:
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Which value of
x
x
x
satisfies the equation
2
3
(
x
−
1
4
)
=
19
6
\frac{2}{3}\left(x-\frac{1}{4}\right)=\frac{19}{6}
3
2
(
x
−
4
1
)
=
6
19
?
\newline
6
6
6
\newline
5
5
5
\newline
−
5
-5
−
5
\newline
−
6
-6
−
6
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Solve for
b
b
b
and simplify your answer.
\newline
−
20
=
5
2
b
-20=\frac{5}{2} b
−
20
=
2
5
b
\newline
Answer:
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Solve for
u
u
u
and simplify your answer.
\newline
4
3
u
=
8
\frac{4}{3} u=8
3
4
u
=
8
\newline
Answer:
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7
÷
(
3
)
/
(
8
)
=
7 \div (3) / (8) =
7
÷
(
3
)
/
(
8
)
=
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7
÷
(
3
)
/
(
8
)
=
7 \div (3) / (8) =
7
÷
(
3
)
/
(
8
)
=
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8
÷
2
(
2
+
2
)
=
8 \div 2(2+2)=
8
÷
2
(
2
+
2
)
=
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Evaluate. Write your answer as a whole number or as a simplified fraction.
\newline
(
3
8
)
/
(
3
4
)
=
(3^{8})/(3^{4})=
(
3
8
)
/
(
3
4
)
=
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5
÷
2
(
1
+
2
)
=
5 \div 2(1+2)=
5
÷
2
(
1
+
2
)
=
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1
2
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