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Grade 7
Powers with negative bases
12(2)\slash(8)-10(5)\slash(6)=
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(
4
0
+
4
−
1
)
×
2
2
(4^{0} + 4^{-1}) \times 2^{2}
(
4
0
+
4
−
1
)
×
2
2
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−
5
2
−
2
\frac{-5}{2}-2
2
−
5
−
2
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4
3
÷
8
+
8
=
4^{3} \div 8+8=
4
3
÷
8
+
8
=
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x+\(1)^
2
2
2
\
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Evaluate.
\newline
(
−
4
)
2
=
(-4)^2 =
(
−
4
)
2
=
_____
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0
=
sin
(
t
2
2
)
0=\sin \left(\frac{t^{2}}{2}\right)
0
=
sin
(
2
t
2
)
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If the sum of three consecutive even integers is
78
78
78
, what is the first of the three even integers? (Hint: If
x
x
x
and
x
+
2
x+2
x
+
2
represent the first two consecutive even integers, then how would the third consecutive even integer be represented?)
\newline
ion
5
5
5
\newline
The first of the three even integers is
□
\square
□
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exttt{
−
11
-11
−
11
+(
−
9
-9
−
9
)=}
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−
55
=
1
4
X
3
+
73
-55 = \frac{1}{4}X^{3} + 73
−
55
=
4
1
X
3
+
73
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Add by using a calculator.
\newline
97
+
(
−
189
)
+
184
+
(
−
98
)
=
97+(-189)+184+(-98)=
97
+
(
−
189
)
+
184
+
(
−
98
)
=
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3
x
−
(
x
+
7
)
=
9
3 x-(x+7)=9
3
x
−
(
x
+
7
)
=
9
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41
100
=
\frac{41}{100}=
100
41
=
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15
3
4
−
10
1
2
=
15 \frac{3}{4}-10 \frac{1}{2}=
15
4
3
−
10
2
1
=
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Solve
3
n
2
=
9
n
3 n^{2}=9 n
3
n
2
=
9
n
.
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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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(
3
2
+
9
)
×
(
[
1
+
9
]
×
2
)
\left(3^{2}+9\right) \times([1+9] \times 2)
(
3
2
+
9
)
×
([
1
+
9
]
×
2
)
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2
log
3
(
x
+
5
)
=
4
2\log_{3}(x+5)=4
2
lo
g
3
(
x
+
5
)
=
4
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Next whole number after
12
2
3
122_{3}
12
2
3
in the base three system
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7
12
=
\frac{7}{12}=
12
7
=
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(
−
28
−
11
)
+
(
−
19
−
17
)
=
(-28-11)+(-19-17)=
(
−
28
−
11
)
+
(
−
19
−
17
)
=
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2
(
1
3
2
)
=
2\left(\frac{1}{3^{2}}\right)=
2
(
3
2
1
)
=
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1
1
1
)
x
2
−
4
=
−
3
\frac{x}{2}-4=-3
2
x
−
4
=
−
3
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\frac{(\(7\)^\(2\)\(-9\))}{\(8\)})\(2=\
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cube of the binomial
(
5
m
−
n
)
(5m-n)
(
5
m
−
n
)
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4
4
4
)
(
−
9
)
÷
(
−
3
)
=
(-9) \div(-3)=
(
−
9
)
÷
(
−
3
)
=
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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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47
(
x
2
×
11
)
=
7
47 (x^2 \times 11) =7
47
(
x
2
×
11
)
=
7
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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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\sqrt{\(5\)}\(-3)^
3
3
3
\
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2
2
2
.
24
3
1
5
=
243^{\frac{1}{5}}=
24
3
5
1
=
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9
×
2
3
=
9 \times \frac{2}{3}=
9
×
3
2
=
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क)
5
4
×
8
×
16
2
5
×
125
\frac{5^{4} \times 8 \times 16}{2^{5} \times 125}
2
5
×
125
5
4
×
8
×
16
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1
1
1
)
(
+
2
)
−
(
−
4
)
=
6
(+2)-(-4)=6
(
+
2
)
−
(
−
4
)
=
6
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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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(
1
1
1
)
9
×
(
4
−
2
)
9 \times(4-2)
9
×
(
4
−
2
)
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7
−
3
z
=
3
+
c
z
\sqrt{7-3 z}=3+c z
7
−
3
z
=
3
+
cz
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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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(
4
x
y
)
2
(4 x y)^{2}
(
4
x
y
)
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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(
3
3
+
4
3
)
2
(3^3+4^3)^2
(
3
3
+
4
3
)
2
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−
4
\sqrt{-4}
−
4
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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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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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5
×
(
a
+
b
+
c
)
=
5\times(a+b+c)=
5
×
(
a
+
b
+
c
)
=
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1
2
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