Exponents and Powers Test

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Exponents and Powers Test - 14

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Weekly Quiz Competition

Question 1
1 / -0

The value of $$\displaystyle \left (-4 \right ) ^{3}\times \left ( -3 \right )^{3}$$ is _____?

A
$$\displaystyle 12^{3}$$

B
$$\displaystyle -12^{3}$$

C
$$\displaystyle -7^{3}$$

D
$$\displaystyle 7^{3}$$

Solution

$$\displaystyle \left ( -4 \right )^{3}\times \left ( -3 \right )^{3}=\left ( -4\times -3 \right )^{3}$$

$$=\displaystyle \left ( -4\times -3 \right )^{3}$$
$$=\displaystyle 12^3$$
Question 2
1 / -0

Find the expression which equals $$\displaystyle a^{x}\times b^{x}$$.

A
$$\left [\displaystyle a^{x}+ b^{x} \right ]$$

B
$$\displaystyle \left ( ab\right )^x $$

C
$$\displaystyle \left (a+b \right )^{x} $$

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

Solution

$$\displaystyle a^{x}\times b^{x}=\left ( ab \right )^{x}$$
So, option $$B$$ is correct.
Question 3
1 / -0

Given that $$2^h\times 2^3 = 2^9$$, find the value of h.

A
$$3$$

B
$$6$$

C
$$8$$

D
$$12$$

Solution

$$2^{h}\times 2^{3}=2^{9}$$
$$\Rightarrow 2^{h+3}=2^{9}$$
$$\Rightarrow h+3=9$$
$$\Rightarrow \boxed{h=6}$$
Question 4
1 / -0

Which option has same value as $$10+10^3$$

A
$$2.0\times 10^3$$

B
$$8.0\times 10^3$$

C
$$4.0\times 10^1$$

D
$$1.01\times 10^3$$

Solution

$$10+{ 10 }^{ 3 }=10+1000=1010=1.01\times { 10 }^{ 3 }$$
So correct answer will be option D
Question 5
1 / -0

If $$12^{5} = 3^{t}\times 4^{t}$$, calculate the value of $$t$$.

A
$$2.5$$

B
$$5$$

C
$$10$$

D
$$20$$

E
$$25$$

Solution

Given $${ 12 }^{ 5 }={ 3 }^{ t }\times { 4 }^{ t }$$
If two terms have same power and they are multiplied then the power can be taken as common
$$\Rightarrow$$ $${ 12 }^{ 5 }={ (3\times 4) }^{ t }$$
$$\Rightarrow$$ $${12}^{5} = {12}^{t}$$
If two terms have same base , then we can equate their powers
$$\Rightarrow$$ $$t=5$$
Question 6
1 / -0

If $$5^{n} \div 5^{3} = 5^{7}$$, then find the value of $$n$$.

A
$$3$$

B
$$4$$

C
$$5$$

D
$$7$$

E
$$10$$

Solution

Given, $${ 5 }^{ n }\div { 5 }^{ 3 }={ 5 }^{ 7 }$$
$$\Rightarrow { 5 }^{ n-3 }={ 5 }^{ 7 }$$ (In case of division of same base exponents get subtracted)
$$\Rightarrow n-3=7$$ (When base is same exponents will be equal)
$$\Rightarrow n=10$$
Question 7
1 / -0

If $$7^{10}= 7 \times 7^n$$, what is the value of $$n$$?

A
$$10$$

B
$$9$$

C
$$7$$

D
$$5$$

E
$$3$$

Solution

Given, $${ 7 }^{ 10 }={ 7 }^{ 1 }\times { 7 }^{ n }$$
$$\Rightarrow 7^{10}={ 7 }^{ 1+n }$$.
$$\Rightarrow 10 = 1+n$$ (as bases are equal, their powers must be equal)
$$\Rightarrow n = 9$$
Question 8
1 / -0

Simplify the following:
$${ (-2) }^{ 7 }\times { (-2) }^{ 3 }\times { (-2) }^{ 4 }$$

A
$${(-2)}^{14}$$

B
$${(-2)}^{24}$$

C
$${(-2)}^{54}$$

D
None of these

Solution

we know,

$$a^{m}*a^{n}=a^{m+n}$$

$$\implies$$ $$a^{m}*a^{n}*a^{p}=a^{m+n+p}$$
so,

$${ (-2) }^{ 7 }\times { (-2) }^{ 3 }\times { (-2) }^{ 4 }$$

$$=(-2)^{7+3+4}$$

$$=(-2)^{14}$$
Question 9
1 / -0

Simplify the following:
$${ \left( \cfrac { 1 }{ 2 } \right) }^{ 4 }\times { \left( \cfrac { 1 }{ 2 } \right) }^{ 5 }\times { \left( \cfrac { 1 }{ 2 } \right) }^{ 6 }$$

A
$${ \left( \cfrac { 1 }{ 2 } \right) }^{ 15 }$$

B
$${ \left( \cfrac { 1 }{ 2 } \right) }^{ 5 }$$

C
$${ \left( \cfrac { 1 }{ 2 } \right) }^{ 10 }$$

D
None of these

Solution

we know,
$$a^{m}*a^{n}=(a)^{m+n}$$
so,
$${ \left( \cfrac { 1 }{ 2 } \right) }^{ 4 }\times { \left( \cfrac { 1 }{ 2 } \right) }^{ 5 }$$
$$=\left(\cfrac12\right)^6$$
so,

$${ \left( \cfrac { 1 }{ 2 } \right) }^{ 4+5+6 } $$
$$=\left(\cfrac12\right)^{15}$$
Question 10
1 / -0

Write $$50000+4000+20+9$$ in standard form.

A
$$54290$$

B
$$5429$$

C
$$54209$$

D
$$54029$$

Solution

We need to write it in a standard form:
$$50000+4000+20+9$$
$$=54000+20+9$$
$$=54020+9$$
$$=54029$$
Ans-Option $$D$$.

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Re-Attempt Weekly Quiz Competition

Exponents and Powers Test - 14

Result

Exponents and Powers Test - 14

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SHARING IS CARING

Question 1

$$\displaystyle 12^{3}$$

$$\displaystyle -12^{3}$$

$$\displaystyle -7^{3}$$

$$\displaystyle 7^{3}$$

Solution

Question 2

$$\left [\displaystyle a^{x}+ b^{x} \right ]$$

$$\displaystyle \left ( ab\right )^x $$

$$\displaystyle \left (a+b \right )^{x} $$

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

Solution

Question 3

$$3$$

$$6$$

$$8$$

$$12$$

Solution

Question 4

$$2.0\times 10^3$$

$$8.0\times 10^3$$

$$4.0\times 10^1$$

$$1.01\times 10^3$$

Solution

Question 5

$$2.5$$

$$5$$

$$10$$

$$20$$

$$25$$

Solution

Question 6

$$3$$

$$4$$

$$5$$

$$7$$

$$10$$

Solution

Question 7

$$10$$

$$9$$

$$7$$

$$5$$

$$3$$

Solution

Question 8

$${(-2)}^{14}$$

$${(-2)}^{24}$$

$${(-2)}^{54}$$

None of these

Solution

Question 9

$${ \left( \cfrac { 1 }{ 2 } \right) }^{ 15 }$$

$${ \left( \cfrac { 1 }{ 2 } \right) }^{ 5 }$$

$${ \left( \cfrac { 1 }{ 2 } \right) }^{ 10 }$$

None of these

Solution

Question 10

$$54290$$

$$5429$$

$$54209$$

$$54029$$

Solution

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