Exponents and Powers Test

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Exponents and Powers Test - 10

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Weekly Quiz Competition

Question 1
1 / -0

$$\displaystyle{10} ^{6} $$ is expanded by writing - number of zeros after 1 -

A
$$0$$

B
$$6$$

C
$$10$$

D
None of these

Solution

$$10^6=1000000$$
6 zeroes are present after 1 in $$\displaystyle {10} ^{6}$$
Question 2
1 / -0

Which of the following expresses product law of exponents?

A
$$(a^{m})^{n} = a^{mn}$$

B
$$a^{m}\times a^{n} = a^{m+n}$$

C
$$a^{m} \div a^{n} = a^{m-n}$$

D
$$a^{m}\div b^{m} = \left (\dfrac {a}{b}\right )^{m}$$

Solution

The product law of exponents states that,
when multiplying two powers that have the same base,
we can add their exponents.
$$\therefore a^{m}\times a^{n} = a^{m+n}$$
So, option $$B$$ is correct.
Question 3
1 / -0

Which of the following expresses zero law of exponents?

A
$$0^{x} = 0$$

B
$$x^{0} = 1$$

C
$$x^{1} = x$$

D
None of the above

Solution

According to the zero law of exponents,
any non - zero number raised to the power of zero is equal to $$1$$.
$$\therefore x^{0} = 1$$, where $$x\neq 0$$
So, option $$B$$ is correct.
Question 4
1 / -0

$$4\times 4^{10}$$ is represented as:

A
$$4^{40}$$

B
$$4^{10}$$

C
$$4^{11}$$

D
$$16^{10}$$

Solution

$$4\times 4^{10} = 4^{1 + 10}$$$$= 4^{11}$$
So, option $$C$$ is correct.
Question 5
1 / -0

Which of the following expresses the power of quotient rule?

A
$$\left (\dfrac {a}{b}\right )^{m} = \dfrac {a^{m}}{b^{m}}$$

B
$$\left (\dfrac {a}{b}\right )^{m} = \left (\dfrac {a}{b}\right )^{m}$$

C
$$\left (\dfrac {a}{b}\right )^{m} = \dfrac {a^{m}}{b}$$

D
$$\left (\dfrac {a}{b}\right )^{m} = \dfrac {a^{m}}{b^{-m}}$$

Solution

If the division of two bases is powered by the same exponent, then the result is division of both the bases, each powered by the given exponent.

$$\therefore\ \bigg (\dfrac {a}{b}\bigg )^{m} = \dfrac {a^{m}}{b^{m}}$$
Question 6
1 / -0

The value of $$x^{a} \div x^{b}$$ is

A
$$x^{\tfrac{a}{b}}$$

B
$$x^{a-b}$$

C
$$x^{ab}$$

D
$$x^{a+b}$$

Solution

$$x^{a} \div x^{b} = \dfrac {x^{a}}{x^{b}} = x^{a-b}$$.
This is the quotient law of exponents.
So, option $$B$$ is correct.
Question 7
1 / -0

How can $$9^{10}\div 9^{1}$$ be represented as?

A
$$9$$

B
$$9^{9}$$

C
$$9^{-9}$$

D
$$9^{10}$$

Solution

$$9^{10}\div 9^{1} = 9^{10-1} = 9^{9}$$

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

What is the value of $$(-6)^{7} \div (-6)^{5}$$?

A
$$36$$

B
$$-36$$

C
$$216$$

D
$$-216$$

Solution

$$(-6)^{7} \div (-6)^{5} = \dfrac {(6)^{7}}{(6)^{5}} = (-6)^{7-5} = (-6)^{2} = 36$$

So, option $$A$$ is correct.
Question 9
1 / -0

Which of the following expresses power law of exponents?

A
$$(a^{m})^{n} = a^{mn}$$

B
$$a^{m}\times b^{m} = (ab)^{m}$$

C
$$a^{m}\times a^{n} = a^{m+n}$$

D
$$a^{0} = 1$$

Solution

The power law states that to raise a power to a power, just multiply the exponents.
$$\therefore (a^{m})^{n} = a^{m\times n}$$
$$= a^{mn}$$
So, option $$A$$ is correct.
Question 10
1 / -0

Which of the following expresses quotient law of exponents?

A
$$a^{m} \times a^{n} = a^{m+n}$$

B
$$a^{m} \div a^{n} = a^{m+n}$$

C
$$a^{m} \times b^{m} = (ab)^{m}$$

D
$$a^{m} \div a^{n} = a^{m-n}$$

Solution

The quotient law of exponents states that we can divide two powers with the same base by subtracting their exponents.

$$\therefore a^{m} \div a^{n} = \dfrac {a^{m}}{a^{n}} = a^{m-n}$$

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Exponents and Powers Test - 10

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Exponents and Powers Test - 10

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SHARING IS CARING

Question 1

$$0$$

$$6$$

$$10$$

None of these

Solution

Question 2

$$(a^{m})^{n} = a^{mn}$$

$$a^{m}\times a^{n} = a^{m+n}$$

$$a^{m} \div a^{n} = a^{m-n}$$

$$a^{m}\div b^{m} = \left (\dfrac {a}{b}\right )^{m}$$

Solution

Question 3

$$0^{x} = 0$$

$$x^{0} = 1$$

$$x^{1} = x$$

None of the above

Solution

Question 4

$$4^{40}$$

$$4^{10}$$

$$4^{11}$$

$$16^{10}$$

Solution

Question 5

$$\left (\dfrac {a}{b}\right )^{m} = \dfrac {a^{m}}{b^{m}}$$

$$\left (\dfrac {a}{b}\right )^{m} = \left (\dfrac {a}{b}\right )^{m}$$

$$\left (\dfrac {a}{b}\right )^{m} = \dfrac {a^{m}}{b}$$

$$\left (\dfrac {a}{b}\right )^{m} = \dfrac {a^{m}}{b^{-m}}$$

Solution

Question 6

$$x^{\tfrac{a}{b}}$$

$$x^{a-b}$$

$$x^{ab}$$

$$x^{a+b}$$

Solution

Question 7

$$9$$

$$9^{9}$$

$$9^{-9}$$

$$9^{10}$$

Solution

Question 8

$$36$$

$$-36$$

$$216$$

$$-216$$

Solution

Question 9

$$(a^{m})^{n} = a^{mn}$$

$$a^{m}\times b^{m} = (ab)^{m}$$

$$a^{m}\times a^{n} = a^{m+n}$$

$$a^{0} = 1$$

Solution

Question 10

$$a^{m} \times a^{n} = a^{m+n}$$

$$a^{m} \div a^{n} = a^{m+n}$$

$$a^{m} \times b^{m} = (ab)^{m}$$

$$a^{m} \div a^{n} = a^{m-n}$$

Solution

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