Exponents and Powers Test

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Exponents and Powers Test - 21

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Weekly Quiz Competition

Question 1
1 / -0

The value of $$3^5 \div3^{-6}$$ is

A
$$3^5$$

B
$$3^{-6}$$

C
$$3^{11}$$

D
$$3^{-11}$$

Solution

We will use, law of exponent $$a^m \div a^n =a^{m-n}$$
Therefore , $$3^5+3^{-6}=3^{5-(-6)}=3^{5+6}=3^{11}$$
Question 2
1 / -0

For a non-zero integer $$x, (x^4)^{-3}$$ is equal

A
$$x^{12}$$

B
$$x^{-12}$$

C
$$x^{64}$$

D
$$x^{-64}$$

Solution

Using law of exponent $$(x^m)^n =(x)^{m\times n}=(x)^{mn}$$
$$(x^4)^{-3}=(x)^{4\times-3}=(x)^{-12}$$
Question 3
1 / -0

If $$x$$ be any integer different from zero and $$m,n$$ be any integers then $$({x^m})^n$$ is equal

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

B
$$x^{mn}$$

C
$$\dfrac {m}{x^n}$$

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

Solution

$$(a^m)^n =(a)^{m+n}$$
[Where,$$a$$ is non-zero integer]
Similarly, $$(x^m)^n =(x)^{m\times n}=(x)^{mn}$$
Question 4
1 / -0

For a non-zero integer $$x, x^{12} \div x^{7}$$ is equal to

A
$$x^{5}$$

B
$$x^{19}$$

C
$$x^{-5}$$

D
$$x^{-19}$$

Solution

Using law of exponent
$$x^m \div x^n =x^{m-n}$$
$$\Rightarrow x^{12} \div x^{7} =x^{12-7}=x^{5}$$
Question 5
1 / -0

$$\left(\dfrac {1}{10}\right)^0$$ is equal to

A
$$0$$

B
$$\dfrac {1}{10}$$

C
$$1$$

D
$$10$$

Solution

Using law of exponents, $$a^0=1$$
where $$a\neq 1$$
$$\Rightarrow \ \left(\dfrac {1}{10}\right)^0 =1$$
Question 6
1 / -0

By solving $$(6^0 -7^0) \times (6^0+7^0)$$, we get ________.

A
$$1$$

B
$$0$$

C
$$2$$

D
$$-1$$

Solution

$$0$$
$$(6^0 -7^0) \times (6^0+7^0)$$
$$=(1-1) \times (1+1)$$
$$=0\times 2=0$$
Question 7
1 / -0

For any two non-zero rational numbers $$x$$ and $$y, x^4 \div y^4$$ is equal to

A
$$(x\div y)^0$$

B
$$(x\div y)^1$$

C
$$(x\div y)^4$$

D
$$(x\div y)^8$$

Solution

Using law of exponents,
$$\dfrac {a^m}{b^m}=\left(\dfrac {a}{b}\right)^m =(a\div b)^m$$
$$\Rightarrow \ x^4 \div y^4 =\left(\dfrac {x}{y}\right)^4 =(x\div y)^4$$
Question 8
1 / -0

The usual from for $$2.03\times 10^{-5}$$

A
$$0.203$$

B
$$0.00203$$

C
$$203000$$

D
$$0.0000203$$

Solution

Using law of exponents, $$a^{-m}=\dfrac {1}{a^m}$$
$$\Rightarrow \ 2.03\times 10^{-5}=\dfrac {2.03}{10^5}$$
$$\Rightarrow \ 2.03\times 10^{-5}=0.0000203$$
Question 9
1 / -0

$$\left(\dfrac {3}{4}\right)^5 \div \left(\dfrac {5}{3}\right)^5$$ is equal to

A
$$\left(\dfrac {3}{4}\div \dfrac {5}{3}\right)^5$$

B
$$\left(\dfrac {3}{4}\div \dfrac {5}{3}\right)^1$$

C
$$\left(\dfrac {3}{4}\div \dfrac {5}{3}\right)^0$$

D
$$\left(\dfrac {3}{4}\div \dfrac {5}{3}\right)^{10}$$

Solution

Using law of exponents, $$a^m \div b^m =(a\div b)^m$$
$$\therefore \ \left(\dfrac {3}{4}\right)^5\div \left(\dfrac {5}{3}\right)^5 =\left(\dfrac {3}{4}\div \dfrac 53 \right)^5$$
Question 10
1 / -0

For any two non-zero rational numbers $$p, p^{13}\div p^8$$ is equal

A
$$p^5$$

B
$$p^{21}$$

C
$$p^{-5}$$

D
$$p^{-19}$$

Solution

Using law of exponents,
$$a^m +a^n =(a)^{m-n}$$
$$ \ p^{13}\div p^8 $$
$$=(p)^{13-8}$$
$$=p^5$$

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Re-Attempt Weekly Quiz Competition

Exponents and Powers Test - 21

Result

Exponents and Powers Test - 21

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SHARING IS CARING

Question 1

$$3^5$$

$$3^{-6}$$

$$3^{11}$$

$$3^{-11}$$

Solution

Question 2

$$x^{12}$$

$$x^{-12}$$

$$x^{64}$$

$$x^{-64}$$

Solution

Question 3

$$x^{m+n}$$

$$x^{mn}$$

$$\dfrac {m}{x^n}$$

$$x^{m-n}$$

Solution

Question 4

$$x^{5}$$

$$x^{19}$$

$$x^{-5}$$

$$x^{-19}$$

Solution

Question 5

$$0$$

$$\dfrac {1}{10}$$

$$1$$

$$10$$

Solution

Question 6

$$1$$

$$0$$

$$2$$

$$-1$$

Solution

Question 7

$$(x\div y)^0$$

$$(x\div y)^1$$

$$(x\div y)^4$$

$$(x\div y)^8$$

Solution

Question 8

$$0.203$$

$$0.00203$$

$$203000$$

$$0.0000203$$

Solution

Question 9

$$\left(\dfrac {3}{4}\div \dfrac {5}{3}\right)^5$$

$$\left(\dfrac {3}{4}\div \dfrac {5}{3}\right)^1$$

$$\left(\dfrac {3}{4}\div \dfrac {5}{3}\right)^0$$

$$\left(\dfrac {3}{4}\div \dfrac {5}{3}\right)^{10}$$

Solution

Question 10

$$p^5$$

$$p^{21}$$

$$p^{-5}$$

$$p^{-19}$$

Solution

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