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Math Problems
Grade 8
Power of a power: integer bases
Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
1
2
7
)
4
(12^7)^4
(
1
2
7
)
4
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
1
5
)
8
(1^5)^8
(
1
5
)
8
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
3
8
)
3
(3^8)^3
(
3
8
)
3
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
3
8
)
9
(3^8)^9
(
3
8
)
9
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
6
3
)
4
(6^3)^4
(
6
3
)
4
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
5
9
)
8
(5^9)^8
(
5
9
)
8
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
4
7
)
4
(4^7)^4
(
4
7
)
4
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
6
9
)
5
(6^9)^5
(
6
9
)
5
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
8
2
)
4
(8^2)^4
(
8
2
)
4
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
1
0
9
)
6
(10^9)^6
(
1
0
9
)
6
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
3
2
)
5
(3^2)^5
(
3
2
)
5
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
8
5
)
4
(8^5)^4
(
8
5
)
4
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
1
2
2
)
5
(12^2)^5
(
1
2
2
)
5
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
1
1
3
)
3
(11^3)^3
(
1
1
3
)
3
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
2
2
)
5
(2^2)^5
(
2
2
)
5
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
1
2
3
)
6
(12^3)^6
(
1
2
3
)
6
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
1
0
9
)
3
(10^9)^3
(
1
0
9
)
3
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
5
6
)
9
(5^6)^9
(
5
6
)
9
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
4
6
)
2
(4^6)^2
(
4
6
)
2
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
4
2
)
8
(4^2)^8
(
4
2
)
8
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
1
1
9
)
4
(11^9)^4
(
1
1
9
)
4
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
9
8
)
5
(9^8)^5
(
9
8
)
5
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
3
8
)
4
(3^8)^4
(
3
8
)
4
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
4
8
)
2
(4^8)^2
(
4
8
)
2
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
1
1
3
)
8
(11^3)^8
(
1
1
3
)
8
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
5
8
)
9
(5^8)^9
(
5
8
)
9
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
9
6
)
6
(9^6)^6
(
9
6
)
6
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
7
3
)
7
(7^3)^7
(
7
3
)
7
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
6
3
)
2
(6^3)^2
(
6
3
)
2
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Simplify. Express your answer as the given base raised to a single exponent.
\newline
(
1
3
)
8
(1^3)^8
(
1
3
)
8
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Example
9
9
9
: Write the quadratic polynomial, the product and sum of whose zeroes are
(
−
9
2
)
(-\frac{9}{2})
(
−
2
9
)
and
(
−
3
2
)
(-\frac{3}{2})
(
−
2
3
)
respectively. [BASIC/Standard] Solution : We have, product
P
=
−
9
2
P=-\frac{9}{2}
P
=
−
2
9
and sum
S
=
−
3
2
S=-\frac{3}{2}
S
=
−
2
3
.
\newline
:. Required quadratic polynomial,
p
(
x
)
=
k
x
2
−
S
x
+
P
p(x)=k{x^{2}-Sx+P}
p
(
x
)
=
k
x
2
−
S
x
+
P
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Write the quadratic polynomial, the product and sum of whose zeroes are
−
9
2
\frac{-9}{2}
2
−
9
and
−
3
2
\frac{-3}{2}
2
−
3
respectively.
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3
x
−
5
=
7
\sqrt{3x-5}=7
3
x
−
5
=
7
.Solve for `x`
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Distribute to create an equivalent expression with the fewest symbols possible.
\newline
(
1
3
)
(
3
j
+
6
)
=
(\frac{1}{3})(3j+6)=
(
3
1
)
(
3
j
+
6
)
=
\newline
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