Exponents and Powers Test

Result

Exponents and Powers Test - 8

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Weekly Quiz Competition

Question 1
1 / -0

If $$3^{n} = 27$$, then $$3^{n - 2}$$ $$=$$?

A
$$3$$

B
$$\dfrac{1}{3}$$

C
$$\dfrac{1}{9}$$

D
$$9$$

Solution

$$3^{n-2}=3^n\times 3^{-2}$$ $$[\because a^{m+n}=a^m\times a^n ]$$
$$=\cfrac{3^n}{3^2}$$ $$[\because a^{-m}=\dfrac{1}{a^m} ]$$

$$\implies 3^{n-2}=\cfrac{27}{9}$$

Thus, $$3^{n-2}=3$$
Question 2
1 / -0

What is the value of $$2^{0.64}*2^{0.36}$$ ?

A
2

B
1

C
16

D
32

Solution

$$2^{0.64}*2^{0.36} =2^{0.64+0.36} = 2^{1.00} = 2^1=2\\ (\because a^m*a^n=a^{m+n})$$
Question 3
1 / -0

Standard form of
$$900000000000$$ is

A
$$9\times10^{11}$$

B
$$9\times10^8$$

C
$$9\times10^3$$

D
none

Solution

Standard form of $$900000000000=9\times 10^{11} $$
Question 4
1 / -0

$$\sqrt [4]{\sqrt [3]{2^{2}}}$$ equal

A
$$2^{\dfrac {-1}{6}}$$

B
$$2^{-6}$$

C
$$2^{\dfrac {1}{6}}$$

D
$$2^{6}$$

Solution

$$\Rightarrow$$ $$\sqrt[4]{\sqrt[3]{2^2}}$$

$$\Rightarrow$$ $$[(2^2)^\tfrac{1}{3}]^{\tfrac{1}{4}}$$

$$\Rightarrow$$ $$(2)^{2\times \tfrac{1}{3}\times \tfrac{1}{4}}$$

$$\Rightarrow$$ $$2^{\tfrac{1}{6}}$$

$$\therefore$$ $$\sqrt[4]{\sqrt[3]{2^2}}=2^{\tfrac{1}{6}}$$
Question 5
1 / -0

$$(-1)^{11}$$ value is:

A
$$+1$$

B
$$0$$

C
$$-1$$

D
none

Solution

The value of $$ {(-1)}^{11} $$ is
$$={(-1)}^{1+1+1+1+1+1+1+1+1+1+1}$$
$$={(-1)}^{1}\times{(-1)}^{1}\times{(-1)}^{1}\times{(-1)}^{1}\times{(-1)}^{1}\times{(-1)}^{1}\times{(-1)}^{1}\times{(-1)}^{1}\times{(-1)}^{1}\times{(-1)}^{1}\times{(-1)}^{1}$$
$$ = -1$$
As odd power of a negative number results in negative number only.
Question 6
1 / -0

In $$y^c$$, $$y$$ is called the:

A
power

B
exponent

C
base

D
alphabet

Solution

In $$y^c$$, $$y$$ is called $$Base.$$
$$\Rightarrow$$ $$y^c$$ in this expression $$y$$ is base and $$c$$ is power.
Question 7
1 / -0

If m is a positive integer which of the following is not equal to $$\displaystyle (2^{4})^{m}$$?

A
$$\displaystyle 2^{4m}$$

B
$$\displaystyle 4^{2m}$$

C
$$\displaystyle 2^{m}(2^{3m})$$

D
$$\displaystyle 4^{m}(2^{m})$$

Solution

$$\displaystyle \left ( 2^{4} \right )^{m}=2^{4m}$$
$$\displaystyle 4^{2m}=\left ( 2^{2} \right )^{2m}=2^{4m};$$
$$\displaystyle 2^{m}\left ( 2^{3m} \right )=2^{m+3m}=2^{4m};$$
$$\displaystyle 4^{m}\left ( 2^{m} \right )=\left ( 2^{2} \right )^{m}.2^{m}=2^{2m}.2^{m}=2^{3m}\neq 2^{4m}$$
Question 8
1 / -0

The expanded form of $$a^6$$ is

A
$$a\, \times\, 6$$

B
$$a\, \times\, a\, \times\, a\, \times\, a\, \times\, a\, \times\, a$$

C
$$a\, \times\, a\, \times\, a\, \times\, a$$

D
a + a + a + a + a + a

Solution

$$a^6\, =\, a\, \times\, a\, \times\, a\, \times\, a\, \times\, a\, \times\, a$$
Question 9
1 / -0

Value of $$2^4\, \times\, (-3)^2\, \times\, 4^2\, \times\, (-5)^2$$ is

A
-144

B
-5760

C
+5760

D
+57600

Solution

$$2^4\, \times\, (-3)^2\, \times\, 4^2\, \times\, (-5)^2\, =\, 16\, \times\, 9\, \times\, 16\, \times\, 25\, =\, 57600$$
Question 10
1 / -0

Value of $$(62)^2$$ is

A
124

B
-124

C
3244

D
3844

Solution

$$62 \times 62 = 3844$$

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Re-Attempt Weekly Quiz Competition

Exponents and Powers Test - 8

Result

Exponents and Powers Test - 8

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SHARING IS CARING

Question 1

$$3$$

$$\dfrac{1}{3}$$

$$\dfrac{1}{9}$$

$$9$$

Solution

Question 2

2

1

16

32

Solution

Question 3

$$9\times10^{11}$$

$$9\times10^8$$

$$9\times10^3$$

none

Solution

Question 4

$$2^{\dfrac {-1}{6}}$$

$$2^{-6}$$

$$2^{\dfrac {1}{6}}$$

$$2^{6}$$

Solution

Question 5

$$+1$$

$$0$$

$$-1$$

none

Solution

Question 6

power

exponent

base

alphabet

Solution

Question 7

$$\displaystyle 2^{4m}$$

$$\displaystyle 4^{2m}$$

$$\displaystyle 2^{m}(2^{3m})$$

$$\displaystyle 4^{m}(2^{m})$$

Solution

Question 8

$$a\, \times\, 6$$

$$a\, \times\, a\, \times\, a\, \times\, a\, \times\, a\, \times\, a$$

$$a\, \times\, a\, \times\, a\, \times\, a$$

a + a + a + a + a + a

Solution

Question 9

-144

-5760

+5760

+57600

Solution

Question 10

124

-124

3244

3844

Solution

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