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Math Problems
Grade 8
Powers with negative bases
Let
(
−
9
2
)
2
=
(-\frac{9}{2})^2 =
(
−
2
9
)
2
=
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−
15
×
(
−
14
)
=
-15 \times(-14)=
−
15
×
(
−
14
)
=
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Simplifying the Expression:
24
÷
(
8
+
4
2
)
24\div(8+4^{2})
24
÷
(
8
+
4
2
)
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Evaluate.
\newline
−
6
×
(
−
1
)
=
-6 \times(-1)=
−
6
×
(
−
1
)
=
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Evaluate.
\newline
−
2
×
(
−
6
)
=
-2 \times(-6)=
−
2
×
(
−
6
)
=
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−
1
5
6
÷
(
−
3
1
3
)
=
-1 \frac{5}{6} \div\left(-3 \frac{1}{3}\right)=
−
1
6
5
÷
(
−
3
3
1
)
=
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−
1
2
÷
(
−
1
3
8
)
=
-\frac{1}{2} \div\left(-1 \frac{3}{8}\right)=
−
2
1
÷
(
−
1
8
3
)
=
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2
−
3
÷
(
−
1
2
7
)
=
\frac{2}{-3} \div\left(-1 \frac{2}{7}\right)=
−
3
2
÷
(
−
1
7
2
)
=
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−
5
7
÷
(
−
1
1
8
)
=
\frac{-5}{7} \div\left(-1 \frac{1}{8}\right)=
7
−
5
÷
(
−
1
8
1
)
=
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−
2
1
4
÷
(
−
3
1
3
)
=
-2 \frac{1}{4} \div\left(-3 \frac{1}{3}\right)=
−
2
4
1
÷
(
−
3
3
1
)
=
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2
1
3
÷
(
−
3
2
3
)
=
2 \frac{1}{3} \div\left(-3 \frac{2}{3}\right)=
2
3
1
÷
(
−
3
3
2
)
=
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4
1
2
÷
(
−
1
3
7
)
=
4 \frac{1}{2} \div\left(-1 \frac{3}{7}\right)=
4
2
1
÷
(
−
1
7
3
)
=
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−
4
7
÷
1
3
4
=
\frac{-4}{7} \div 1 \frac{3}{4}=
7
−
4
÷
1
4
3
=
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3
−
4
÷
(
−
2
1
3
)
=
\frac{3}{-4} \div\left(-2 \frac{1}{3}\right)=
−
4
3
÷
(
−
2
3
1
)
=
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−
3
1
2
÷
−
5
8
=
-3 \frac{1}{2} \div \frac{-5}{8}=
−
3
2
1
÷
8
−
5
=
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−
1
3
5
÷
5
−
6
=
-1 \frac{3}{5} \div \frac{5}{-6}=
−
1
5
3
÷
−
6
5
=
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2
1
5
÷
4
−
9
=
2 \frac{1}{5} \div \frac{4}{-9}=
2
5
1
÷
−
9
4
=
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−
3
1
2
÷
(
−
1
2
5
)
=
-3 \frac{1}{2} \div\left(-1 \frac{2}{5}\right)=
−
3
2
1
÷
(
−
1
5
2
)
=
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−
2
1
5
÷
−
3
7
=
-2 \frac{1}{5} \div \frac{-3}{7}=
−
2
5
1
÷
7
−
3
=
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−
2
3
4
÷
5
−
9
=
-2 \frac{3}{4} \div \frac{5}{-9}=
−
2
4
3
÷
−
9
5
=
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1
1
8
÷
(
−
3
7
)
=
1 \frac{1}{8} \div\left(-\frac{3}{7}\right)=
1
8
1
÷
(
−
7
3
)
=
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6
×
(
7
−
2
)
=
6 \times(7-2)=
6
×
(
7
−
2
)
=
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15
−
3
2
+
4
=
15-3^{2}+4=
15
−
3
2
+
4
=
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(iii)
(
−
75
)
+
18
=
(-75)+18=
(
−
75
)
+
18
=
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Q
5
−
3
5-3
5
−
3
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(
1
5
)
−
3
=
\left(\frac{1}{5}\right)^{-3}=
(
5
1
)
−
3
=
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6
−
3
=
6^{-3}=
6
−
3
=
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(
1
+
2
)
2
=
(1+2)^2=
(
1
+
2
)
2
=
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Evaluate. Write your answer as a whole number or as a simplified fraction.
\newline
2
9
2
5
=
\frac{2^{9}}{2^{5}}=
2
5
2
9
=
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Solve for all values of
x
x
x
.
\newline
x
9
=
9
x
\frac{x}{9}=\frac{9}{x}
9
x
=
x
9
\newline
Answer:
x
=
x=
x
=
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Factor completely:
\newline
(
2
x
+
3
)
(
4
x
+
9
)
+
(
5
x
+
4
)
(
4
x
+
9
)
(2 x+3)(4 x+9)+(5 x+4)(4 x+9)
(
2
x
+
3
)
(
4
x
+
9
)
+
(
5
x
+
4
)
(
4
x
+
9
)
\newline
Answer:
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Factor completely:
\newline
(
x
−
9
)
(
3
x
+
5
)
+
(
4
x
+
9
)
(
3
x
+
5
)
2
(x-9)(3 x+5)+(4 x+9)(3 x+5)^{2}
(
x
−
9
)
(
3
x
+
5
)
+
(
4
x
+
9
)
(
3
x
+
5
)
2
\newline
Answer:
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Factor completely:
\newline
(
x
+
5
)
(
3
x
+
7
)
+
(
2
x
+
7
)
(
3
x
+
7
)
2
(x+5)(3 x+7)+(2 x+7)(3 x+7)^{2}
(
x
+
5
)
(
3
x
+
7
)
+
(
2
x
+
7
)
(
3
x
+
7
)
2
\newline
Answer:
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Factor completely:
\newline
(
4
x
+
1
)
(
2
x
+
5
)
−
(
4
x
+
1
)
2
(
4
x
+
3
)
(4 x+1)(2 x+5)-(4 x+1)^{2}(4 x+3)
(
4
x
+
1
)
(
2
x
+
5
)
−
(
4
x
+
1
)
2
(
4
x
+
3
)
\newline
Answer:
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Factor completely:
\newline
(
x
+
9
)
(
3
x
−
1
)
−
(
x
+
9
)
2
(
2
x
+
3
)
(x+9)(3 x-1)-(x+9)^{2}(2 x+3)
(
x
+
9
)
(
3
x
−
1
)
−
(
x
+
9
)
2
(
2
x
+
3
)
\newline
Answer:
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Factor completely:
\newline
6
x
(
x
−
5
)
+
7
(
x
−
5
)
6 x(x-5)+7(x-5)
6
x
(
x
−
5
)
+
7
(
x
−
5
)
\newline
Answer:
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Factor completely:
\newline
x
2
(
x
+
3
)
−
7
x
(
x
+
3
)
+
6
(
x
+
3
)
x^{2}(x+3)-7 x(x+3)+6(x+3)
x
2
(
x
+
3
)
−
7
x
(
x
+
3
)
+
6
(
x
+
3
)
\newline
Answer:
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Factor completely:
\newline
6
x
2
(
2
x
−
7
)
−
7
(
2
x
−
7
)
6 x^{2}(2 x-7)-7(2 x-7)
6
x
2
(
2
x
−
7
)
−
7
(
2
x
−
7
)
\newline
Answer:
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Factor completely:
\newline
(
2
x
−
3
)
2
−
(
x
+
1
)
2
(2 x-3)^{2}-(x+1)^{2}
(
2
x
−
3
)
2
−
(
x
+
1
)
2
\newline
Answer:
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Factor completely:
\newline
(
5
x
+
1
)
2
−
(
3
x
+
7
)
2
(5 x+1)^{2}-(3 x+7)^{2}
(
5
x
+
1
)
2
−
(
3
x
+
7
)
2
\newline
Answer:
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Factor completely:
\newline
(
7
x
−
2
)
2
−
(
3
x
−
1
)
2
(7 x-2)^{2}-(3 x-1)^{2}
(
7
x
−
2
)
2
−
(
3
x
−
1
)
2
\newline
Answer:
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Factor completely:
\newline
(
x
−
2
)
2
−
(
6
x
+
5
)
2
(x-2)^{2}-(6 x+5)^{2}
(
x
−
2
)
2
−
(
6
x
+
5
)
2
\newline
Answer:
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Factor completely:
\newline
(
x
−
2
)
2
−
(
2
x
−
7
)
2
(x-2)^{2}-(2 x-7)^{2}
(
x
−
2
)
2
−
(
2
x
−
7
)
2
\newline
Answer:
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Factor completely:
\newline
(
3
x
−
2
)
2
−
(
10
x
−
7
)
2
(3 x-2)^{2}-(10 x-7)^{2}
(
3
x
−
2
)
2
−
(
10
x
−
7
)
2
\newline
Answer:
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Factor completely:
\newline
(
x
+
1
)
2
−
(
2
x
+
5
)
2
(x+1)^{2}-(2 x+5)^{2}
(
x
+
1
)
2
−
(
2
x
+
5
)
2
\newline
Answer:
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Factor completely:
\newline
(
x
−
8
)
6
−
2
(
x
−
8
)
5
(x-8)^{6}-2(x-8)^{5}
(
x
−
8
)
6
−
2
(
x
−
8
)
5
\newline
Answer:
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Factor completely:
\newline
(
x
−
9
)
+
(
x
−
9
)
2
(x-9)+(x-9)^{2}
(
x
−
9
)
+
(
x
−
9
)
2
\newline
Answer:
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Factor completely:
\newline
(
x
+
6
)
3
−
(
x
+
6
)
4
(x+6)^{3}-(x+6)^{4}
(
x
+
6
)
3
−
(
x
+
6
)
4
\newline
Answer:
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Factor completely:
\newline
(
7
x
−
5
)
4
+
9
(
7
x
−
5
)
3
(7 x-5)^{4}+9(7 x-5)^{3}
(
7
x
−
5
)
4
+
9
(
7
x
−
5
)
3
\newline
Answer:
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Factor completely:
\newline
9
(
3
x
−
5
)
6
+
(
3
x
−
5
)
7
9(3 x-5)^{6}+(3 x-5)^{7}
9
(
3
x
−
5
)
6
+
(
3
x
−
5
)
7
\newline
Answer:
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2
3
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