Exponents and Powers Test

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Exponents and Powers Test - 13

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Weekly Quiz Competition

Question 1
1 / -0

The value of $$(100)^{0}$$ is _____.

A
$$1$$

B
$$0$$

C
$$100$$

D
$$1000$$

Solution

According to the law of power of $$0$$,
$$(100)^{0} = 1$$.

So, option $$A$$ is correct.
Question 2
1 / -0

Evaluate: $$({(10)^0} + (12)^{0})\times (18)^{0}$$

A
$$1$$

B
$$0$$

C
$$2$$

D
$$18$$

Solution

$$((10)^{0} + (12)^{0})\times (18)^{0} = (1 + 1) \times 1$$
$$= (2)\times 1$$
$$= 2$$
So. option $$C$$ is correct.
Question 3
1 / -0

The value of $$\displaystyle \left ( 1^{2}+2^{2}+3^{2} \right )^{2}$$ is:

A
$$236$$

B
$$196$$

C
$$189$$

D
$$97$$

Solution

$$\displaystyle \left ( 1^{2}+2^{2}+3^{2} \right )^{2}=(1+4+9)^2$$
=$$14^2$$
=$$196$$
So, option $$B$$ is correct.
Question 4
1 / -0

Simplify: $$\displaystyle \left ( -a \right )^{9}\times \left ( -b \right )^{9}$$

A
$$\displaystyle \left ( ab \right )^{9}$$

B
$$\displaystyle \left ( -ab \right )^{9}$$

C
$$\displaystyle -\left ( ab \right )^{9}$$

D
$$\displaystyle \left ( a-b \right )^{9}$$

Solution

$$(-a)^9 \times (-b)^9 = [ -a \times -b]^9$$

= $$ [ a \times b]^9$$

=$$ (ab)^9$$
So, option $$A$$ is correct.
Question 5
1 / -0

Express $$\displaystyle \left ( 81 \right )^{4}$$ as a power with the base $$3$$.

A
$$\displaystyle 3^{-16}$$

B
$$\displaystyle 3^{16}$$

C
$$\displaystyle 3^{0}$$

D
$$\displaystyle 3^{8}$$

Solution

$$81 ^{4}= \left ( 3^{4} \right )^{4}$$
$$= 3^{4\times4}\quad\quad\quad\because[(a^m)^n=a^{mn}]$$
$$=3^{16}$$

Hence, option $$A$$ is correct.
Question 6
1 / -0

To simplify the following expression correctly, what must be done with the exponents?
$${ { 5 }^{ a }\times { 5 }^{ b }\times }{ 5 }^{ c }$$

A
Add the exponents.

B
Multiply the exponents.

C
Divide the exponents

D
Subtract the exponents.

Solution

Since the base is same, the exponents can be added (Product rule of exponents).
$$\therefore 5^a \times 5^b \times 5^c = 5^{(a+b+c)}$$
Hence, option $$A$$ is correct.
Question 7
1 / -0

$$\displaystyle \left ( 16\div 15 \right )^{3}$$ can also be expressed as:

A
$$\displaystyle 16^{3}\div 15^{3} $$

B
$$\displaystyle 16^{3}\div 15 $$

C
$$\displaystyle 16\div 15^{3} $$

D
$$\displaystyle 15^{3}\div 16^{3} $$

Solution

$$\displaystyle\left ( 16\div 15 \right )^{3}=16^{3}\div 15^{3}$$

This is quotient law of exponents.
Hence, option $$A$$ is correct
Question 8
1 / -0

Evaluate: $$\displaystyle 5^{2}\times 3^{2} $$

A
$$\displaystyle \left (53 \right ) ^{2}$$

B
$$\displaystyle \left (15 \right ) ^{2}$$

C
$$\displaystyle \left (8 \right ) ^{2}$$

D
$$60$$

Solution

$$\displaystyle 5^{2}\times 3^{2}=\left ( 15 \right )^{2}$$
So, option $$B$$ is correct.
Question 9
1 / -0

Solve the following using Product Law of Exponents.
$$a\times { a }^{ 2 }\times { a }^{ \tfrac { 1 }{ 2 } }$$

A
$${ a }^{ 7 }$$

B
$${ a }^{ \tfrac { 2 }{ 7 } }$$

C
$${ a }^{ 3 }$$

D
$${ a }^{ \tfrac { 7 }{ 2 } }$$

Solution

By product law of exponents
$$a\times { a }^{ 2 }\times { a }^{ \tfrac { 1 }{ 2 } } = { a }^{ \left( 1+2+\tfrac { 1 }{ 2 } \right) }$$
$$={ a }^{ \tfrac { 7 }{ 2 } }$$
Therefore option $$D$$ is the correct answer.
Question 10
1 / -0

On simplifying $$\displaystyle 3^{3}\times a^{3}\times b^{3}$$, we get

A
$$\displaystyle \left ( 3ab \right )^{3} $$

B
$$\displaystyle 3\left ( ab \right )^{3} $$

C
$$\displaystyle \left ( 27ab \right )^{3} $$

D
None of these

Solution

$$\displaystyle 3^{2}\times a^{3}\times b^{3}=\left ( 3ab \right )^{3}$$.
This is the power of product law of exponents.
So, option $$A$$ is correct.

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Re-Attempt Weekly Quiz Competition

Exponents and Powers Test - 13

Result

Exponents and Powers Test - 13

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SHARING IS CARING

Question 1

$$1$$

$$0$$

$$100$$

$$1000$$

Solution

Question 2

$$1$$

$$0$$

$$2$$

$$18$$

Solution

Question 3

$$236$$

$$196$$

$$189$$

$$97$$

Solution

Question 4

$$\displaystyle \left ( ab \right )^{9}$$

$$\displaystyle \left ( -ab \right )^{9}$$

$$\displaystyle -\left ( ab \right )^{9}$$

$$\displaystyle \left ( a-b \right )^{9}$$

Solution

Question 5

$$\displaystyle 3^{-16}$$

$$\displaystyle 3^{16}$$

$$\displaystyle 3^{0}$$

$$\displaystyle 3^{8}$$

Solution

Question 6

Add the exponents.

Multiply the exponents.

Divide the exponents

Subtract the exponents.

Solution

Question 7

$$\displaystyle 16^{3}\div 15^{3} $$

$$\displaystyle 16^{3}\div 15 $$

$$\displaystyle 16\div 15^{3} $$

$$\displaystyle 15^{3}\div 16^{3} $$

Solution

Question 8

$$\displaystyle \left (53 \right ) ^{2}$$

$$\displaystyle \left (15 \right ) ^{2}$$

$$\displaystyle \left (8 \right ) ^{2}$$

$$60$$

Solution

Question 9

$${ a }^{ 7 }$$

$${ a }^{ \tfrac { 2 }{ 7 } }$$

$${ a }^{ 3 }$$

$${ a }^{ \tfrac { 7 }{ 2 } }$$

Solution

Question 10

$$\displaystyle \left ( 3ab \right )^{3} $$

$$\displaystyle 3\left ( ab \right )^{3} $$

$$\displaystyle \left ( 27ab \right )^{3} $$

None of these

Solution

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