Exponents and Powers Test

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Exponents and Powers Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

The product $$\sqrt [3]{2} . \sqrt [4]{2} . \sqrt [12]{32}$$ equals.

A
$$\sqrt {2}$$

B
$$2$$

C
$$\sqrt [12]{2}$$

D
$$\sqrt [12]{32}$$

Solution

$$\sqrt[3]{2}\times\sqrt[4]{2}\times\sqrt[12]{32}$$
= $${2}^\dfrac{1}{3}\times{2}^\dfrac{1}{4}\times\sqrt[12]{2^5}$$
= $${2}^\dfrac{1}{3}\times{2}^\dfrac{1}{4}\times{2}^\dfrac{5}{12}$$
= $${2}^{\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{5}{12}}$$
= $${2}^{\dfrac{12}{12}}$$
= $${2}$$
Hence, option $$B$$ is the correct answer.
Question 2
1 / -0

Find the value of $$m$$ for which: $$100^{m} \div 100^{4} = 100^{8}$$

A
$$1$$

B
$$2$$

C
$$3$$

D
$$12$$

Solution

$$100^{m}\div 100^{4} = 100^{m-4}$$

Now, we know that $$\dfrac {a^{m}}{a^{n}} = a^{m - n}$$
$$\therefore m - 4 = 8$$
$$\therefore m = 12$$
Upon, verifying, $$100^{12} \div 100^{4} = 100^{12-4} = 100^{8}$$

So, option $$D$$ is correct.
Question 3
1 / -0

Fill in the blanks:
$$10^{8}$$ is expanded by writing _____ number of zeros after $$1$$.

A
$$8$$

B
$$0$$

C
$$10$$

D
none

Solution

$$10^{8}$$ means $$10$$ is to be multiplied $$8$$ times with itself.
Therefore, it means that when we expand $$10^8$$, there will be $$8$$ zeros after 1.
Question 4
1 / -0

Find the value of $$x$$ for which $$(50^{3})^{x} = (50^{24})$$

A
$$8$$

B
$$6$$

C
$$21$$

D
$$18$$

Solution

$$(50^{3})^{x} = 50^{3x}$$
Also, $$50^{3x} = 50^{24}$$
$$\therefore 3x = 24$$
$$\therefore x = 8$$
So, option $$A$$ is correct.
Question 5
1 / -0

Find the value of $$m$$, such that $$(-2^{m})^{6} = (-2)^{60}$$

A
$$-10$$

B
$$6$$

C
$$10$$

D
$$-6$$
Question 6
1 / -0

How many non zero and positive real numbers x are there such that $$x^{x^\sqrt x} = (x \sqrt x )^x$$?

A
1

B
2

C
4

D
infinite

Solution

Given:
$$\displaystyle x^{x^{3/2}} = x^{\displaystyle \frac{3x}{2}}$$

Case - I when base $$x = 1$$ then LHS = RHS = 1

Case - II when base $$x$$ $$\neq$$ 1

then $$\displaystyle x^{3/2} = \frac{3x}{2}$$

$$\Rightarrow x \displaystyle \left ( \sqrt x - \frac{3}{2} \right ) = 0$$

$$\Rightarrow x \neq 0 \therefore \sqrt x = \displaystyle \frac{3}{2}$$

$$\Rightarrow x = \dfrac{9}{4}$$

Hence two solutions
Question 7
1 / -0

Simplify: $$5^{4} \div 5^{3}$$

A
$$5^{12}$$

B
$$5^{7}$$

C
$$5$$

D
$$\dfrac {1}{5}$$

Solution

$$5^{4}\div 5^{3} = \dfrac {5^{4}}{5^{3}} = 5^{4-3} = 5^{1} = {5}$$

So option $$C$$ is correct.
Question 8
1 / -0

Find the value of $$(-5^{5})^{3}$$

A
$$(-5)^{8}$$

B
$$(-5)^{15}$$

C
$$(-5)^{10}$$

D
$$5^{15}$$

Solution

$$(-5^{5})^{3} = (-5)^{15}$$
So, option $$B$$ is correct.
Question 9
1 / -0

Find the value of: $$[(-4^{2})^{3}]^{2}$$

A
$$(-4)^{-12}$$

B
$$4^{-12}$$

C
$$4^{12}$$

D
$$(-4)^{7}$$

Solution

$$[(-4^{2})^{3}]^{2} = [(-4)^{6}]^{2}$$

$$= [(-4)^{12}]$$

$$= (4)^{12}$$ $$\left(\because (-4)^{12} = (-1)^{12}\times (4)^{12} = 1\times 4^{12}\right)$$

So, option $$C$$ is correct.
Question 10
1 / -0

Place the following numbers with the given labels in order of greatest to least.

$$F={({10}^{10})}^{10}$$

$$G={10}^{10}$$ $${10}^{10}$$

$$H=\cfrac{{10}^{100}}{{10}^{10}}$$

$$I=100$$

A
$$F,G,H,I$$

B
$$G,F,H,I$$

C
$$F,H,G,I$$

D
$$H,F,G,I$$

Solution

$$F={({10}^{10})}^{10}$$$$=10^{10\times 10}$$$$=10^{100}$$

$$G={10}^{10}$$ $${10}^{10}$$$$=10^{10+10}$$$$=10^{20}$$

$$H=\cfrac{{10}^{100}}{{10}^{10}}$$$$=10^{100-10}$$$$=10^{90}$$

$$I=100$$

Clearly $$F>H>G>I$$

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Re-Attempt Weekly Quiz Competition

Exponents and Powers Test - 19

Result

Exponents and Powers Test - 19

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SHARING IS CARING

Question 1

$$\sqrt {2}$$

$$2$$

$$\sqrt [12]{2}$$

$$\sqrt [12]{32}$$

Solution

Question 2

$$1$$

$$2$$

$$3$$

$$12$$

Solution

Question 3

$$8$$

$$0$$

$$10$$

none

Solution

Question 4

$$8$$

$$6$$

$$21$$

$$18$$

Solution

Question 5

$$-10$$

$$6$$

$$10$$

$$-6$$

Question 6

1

2

4

infinite

Solution

Question 7

$$5^{12}$$

$$5^{7}$$

$$5$$

$$\dfrac {1}{5}$$

Solution

Question 8

$$(-5)^{8}$$

$$(-5)^{15}$$

$$(-5)^{10}$$

$$5^{15}$$

Solution

Question 9

$$(-4)^{-12}$$

$$4^{-12}$$

$$4^{12}$$

$$(-4)^{7}$$

Solution

Question 10

$$F,G,H,I$$

$$G,F,H,I$$

$$F,H,G,I$$

$$H,F,G,I$$

Solution

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