Exponents and Powers Test

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Exponents and Powers Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

If $$\left(\dfrac{3}{2}\right)^2 \times \left(\dfrac{3}{2}\right)^{a+5}=\left(\dfrac{3}{2}\right)^8$$, then $$a =$$______ .

A
$$-1$$

B
$$0$$

C
$$1$$

D
$$2$$

Solution

$$\left(\dfrac{3}{2}\right)^2\times\left(\dfrac{3}{2}\right)^{a+5}=\left(\dfrac{3}{2}\right)^8\Rightarrow \left(\dfrac{3}{2}\right)^{a+7}=\left(\dfrac{3}{2}\right)^8$$
On comparing, we get, $$a+7=8 \Rightarrow a=1$$
Question 2
1 / -0

Which expression is equivalent to $$(9^{ \ 2})$$

A
$$-81$$

B
$$\dfrac{1}{81}$$

C
$$81$$

D
none of these

Solution

Now,
$$9^{2}=9\times 9$$
$$=81$$
Question 3
1 / -0

$${ \left( \dfrac { 2 }{ 3 } \right) }^{ 0 }=?$$

A
$$\dfrac{3}{2}$$

B
$$\dfrac{2}{3}$$

C
$$1$$

D
$$0$$

Solution

Given $${ \left( \dfrac { 2 }{ 3 } \right) }^{ 0 }$$
By using tha law of exponents i.e., $$\left(\dfrac{a}{b}\right)^0=1$$
$$\therefore { \left( \dfrac { 2 }{ 3 } \right) }^{ 0 }=1$$
Question 4
1 / -0

If $$x$$ be any non-zero integer and $$m,n$$ be positive integers, then $$x^m \times x^n$$ is equal to

A
$$x^m$$

B
$$x^{m+n}$$

C
$$x^n$$

D
$$x^{m-n}$$

Solution

Using law of exponents,
$$a^m\times a^n =(a)^{m+n}\quad $$ [Where $$a$$ is non-zero integer]
Similarly $$x^m\times x^n =(x)^{m+n}$$
Question 5
1 / -0

If $$x$$ be any non-zero integers, then $$x^{-1}$$ is equal to

A
$$x$$

B
$$\dfrac {1}{x}$$

C
$$-x$$

D
$$\dfrac {-1}{x}$$

Solution

Using law of exponents,
$$a^{-m} =\dfrac {1}{a^m}$$
[Where,$$a$$ is non-zero integer]
Similarly, $$x^{-1}=\dfrac {1}{x}$$
Question 6
1 / -0

If $$y$$ is any non-zero integer, then $$y^0$$ is equal to ....

A
$$1$$

B
$$0$$

C
$$-1$$

D
Not found

Solution

Using the law of exponents, $$a^0 =1$$

Therefore $$y^0=1$$
Question 7
1 / -0

Choose the correct answer from the given four options:
The usual form of $$5.658 \times 10^5$$ is

A
$$5658$$

B
$$56580$$

C
$$565800$$

D
$$5658000$$

Solution

$$5.658 \times 10^5 = 565800$$
Question 8
1 / -0

The standard form of $$751.65$$ is

A
$$7.5165 \times 10^2$$

B
$$75.165 \times 10^1$$

C
$$7.5165 \times 10^4$$

D
$$7.52 \times 10^2$$

Solution

The standard form of $$751.65$$ is,
$$7.5165 \times 10^2\approx7.52\times10^2$$
Question 9
1 / -0

Evaluate the following:
$$ 2.3 \times {10}^{11} + 3.2 \times{10}^{11}$$

A
$$5.2 \times {10}^{11}$$

B
$$5.5 \times {10}^{11}$$

C
$$5.5 \times {10}^{10}$$

D
none of these

Solution

$$ 2.3 \times {10}^{11} +3.2 \times{10}^{11}$$ $$= (2.3 + 3.2) \times {10}^{11}$$ $$= 5.5 \times {10}^{11} $$
$$\therefore$$ B is the correct answer.
Question 10
1 / -0

Which of the following numbers should be added to $$4 \times {10}^5$$ to get $$5.3 \times {10}^5$$?

A
$$3.3 \times {10}^5$$

B
$$1.3 \times {10}^5$$

C
$$2.3 \times {10}^5$$

D
$$7.3 \times {10}^5$$

Solution

Required number will be the subtraction of given two numbers
Hence, the number is given by
$$5.3 \times{10}^5 - 4 \times {10}^5$$ $$= (5.3 - 4) \times {10}^5 $$ $$= 1.3 \times {10}^5$$
Hence, (B) will be correct answer.

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Re-Attempt Weekly Quiz Competition

Exponents and Powers Test - 16

Result

Exponents and Powers Test - 16

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SHARING IS CARING

Question 1

$$-1$$

$$0$$

$$1$$

$$2$$

Solution

Question 2

$$-81$$

$$\dfrac{1}{81}$$

$$81$$

none of these

Solution

Question 3

$$\dfrac{3}{2}$$

$$\dfrac{2}{3}$$

$$1$$

$$0$$

Solution

Question 4

$$x^m$$

$$x^{m+n}$$

$$x^n$$

$$x^{m-n}$$

Solution

Question 5

$$x$$

$$\dfrac {1}{x}$$

$$-x$$

$$\dfrac {-1}{x}$$

Solution

Question 6

$$1$$

$$0$$

$$-1$$

Not found

Solution

Question 7

$$5658$$

$$56580$$

$$565800$$

$$5658000$$

Solution

Question 8

$$7.5165 \times 10^2$$

$$75.165 \times 10^1$$

$$7.5165 \times 10^4$$

$$7.52 \times 10^2$$

Solution

Question 9

$$5.2 \times {10}^{11}$$

$$5.5 \times {10}^{11}$$

$$5.5 \times {10}^{10}$$

none of these

Solution

Question 10

$$3.3 \times {10}^5$$

$$1.3 \times {10}^5$$

$$2.3 \times {10}^5$$

$$7.3 \times {10}^5$$

Solution

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