Exponents and Powers Test

Result

Exponents and Powers Test - 11

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

Which of the following represents the power of product rule?

A
$$(x\times y)^{a} = x^{a} \times y$$

B
$$(x\times y)^{a} = x \times y^{a}$$

C
$$(x\times y)^{a} = x^{a} + y^{a}$$

D
$$(x\times y)^{a} = x^{a} \times y^{a}$$

Solution

If the product of the bases is powered by the same exponent,
then the result is multiplication of all the bases,
each powered by the given exponent.
$$\therefore (x\times y)^{a} = x^{a} \times y^{a}$$.
So, option $$D$$ is correct.
Question 2
1 / -0

Simplify: $$3^{8} \div 3^{5}$$

A
$$-\dfrac {1}{27}$$

B
$$\dfrac {1}{27}$$

C
$$27$$

D
$$-27$$

Solution

$$3^{8} \div 3^{5} = \dfrac {3^{8}}{3^{5}} = 3^{8-5} = 3^{3} = 27$$

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

Which of the following can also be represented as $$a^{mn}$$?

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

B
$$(a^{m})^{n}$$

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

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

Solution

$$a^{mn} = (a^{m})^{n}$$.
This is the power law of exponents.
So, option $$B$$ is correct.
Question 4
1 / -0

In simplified form, $$((3)^{0} + (5)^{0})^{0}$$ is equal to:

A
$$2$$

B
$$1$$

C
$$0$$

D
$$8$$

Solution

$$(3^{0} + 5^{0})^{0} = (1 + 1)^{0}$$

$$= (2)^{0}$$ $$= 1$$

So, option $$B$$ is correct.
Question 5
1 / -0

What is the value of $$10^{107} \div 10^{103}$$?

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

B
$$\dfrac {1}{100}$$

C
$${10,000}$$

D
$$\dfrac {1}{1000}$$

Solution

$$10^{107} \div 10^{103} = 10^{107 - 103} = 10^{4} = {10000}$$

So, option $$C$$ is correct.
Question 6
1 / -0

$$\dfrac {(-8)^{15}}{(-8)^{12}}$$ is equal to:

A
$$512$$

B
$$-512$$

C
$$256$$

D
$$-256$$

Solution

$$\dfrac {(-8)^{15}}{(-8)^{12}} = (-8)^{15 -12} = (-8)^{3} = -512$$

So, option $$B$$ is correct.
Question 7
1 / -0

Which of the following statement/s is/are true?

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

B
$$(a^{m})^{n} = (a^{m+n}) = (a^{m-n})$$

C
$$(a^{m})^{n} = (a^{n-m}) = (a^{n})^{m}$$

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

Solution

$$(a^{m})^{n} = a^{mn}$$
$$(a^{n})^{m} = a^{nm} = a^{mn}$$
$$\therefore (a^{m})^{n} = (a^{mn}) = (a^{n})^{m}$$

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

Evaluate: $$\left (\dfrac {2^{3}}{3^{3}} \right )^{2}$$

A
$$\dfrac {64}{729}$$

B
$$\dfrac {729}{64}$$

C
$$\dfrac {32}{243}$$

D
$$\dfrac {243}{32}$$

Solution

$$\left (\dfrac {2^{3}}{3^{3}} \right )^{2} = \dfrac {2^{6}}{3^{6}} = \dfrac {64}{729}$$

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

The value of $$(2^{6})^{2}$$ is

A
$$256$$

B
$$4096$$

C
$$1028$$

D
$$512$$

Solution

$$(2^{6})^{2} = 2^{6\times 2}$$ $$[$$By using $$(a^m)^n=a^{m\times n}]$$
$$ = 2^{12}$$
$$ = 4096$$

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

The value of $$21^{0}$$ is _____.

A
$$0$$

B
$$21$$

C
$$1$$

D
$$-21$$

Solution

$$21^{0} = 1$$
$$\because a^{0} = 1$$
This is the law for zero exponent.
So, option $$C$$ is correct.

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Exponents and Powers Test - 11

Result

Exponents and Powers Test - 11

Score

-

Rank

-

SHARING IS CARING

Question 1

$$(x\times y)^{a} = x^{a} \times y$$

$$(x\times y)^{a} = x \times y^{a}$$

$$(x\times y)^{a} = x^{a} + y^{a}$$

$$(x\times y)^{a} = x^{a} \times y^{a}$$

Solution

Question 2

$$-\dfrac {1}{27}$$

$$\dfrac {1}{27}$$

$$27$$

$$-27$$

Solution

Question 3

$$a^{m+n}$$

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

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

$$a^{m-n}$$

Solution

Question 4

$$2$$

$$1$$

$$0$$

$$8$$

Solution

Question 5

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

$$\dfrac {1}{100}$$

$${10,000}$$

$$\dfrac {1}{1000}$$

Solution

Question 6

$$512$$

$$-512$$

$$256$$

$$-256$$

Solution

Question 7

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

$$(a^{m})^{n} = (a^{m+n}) = (a^{m-n})$$

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

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

Solution

Question 8

$$\dfrac {64}{729}$$

$$\dfrac {729}{64}$$

$$\dfrac {32}{243}$$

$$\dfrac {243}{32}$$

Solution

Question 9

$$256$$

$$4096$$

$$1028$$

$$512$$

Solution

Question 10

$$0$$

$$21$$

$$1$$

$$-21$$

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.