Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

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If Expression of $216$ as a product of its prime factors is $2 \times 2 \times 2 \times 3 \times 3 \times k$ , then $k =$

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Important Questions on Exponents and Powers

EASY

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

What is the number of digits in

7^{25}

,

8^{23}

and

9^{20}

respectively? [Given

\log_{10} (2) = 0.301

,

\log_{10} (3) = 0.477

,

\log_{10} (7) = 0.845

]

EASY

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

If $a, m and n$ are rational numbers, then $a^{m} \times a^{n} = a^{p}$ . Then the value of $p =$ _____.

EASY

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

What is the number of digit in

2^{40}

? (Given that

\log_{10} 2 = 0.301

)

EASY

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

If

4^{x} . 8^{y} = 128

and

\frac{3^{x}}{27^{y}} = \frac{1}{3}

, then find the values of

x

and

y

.

EASY

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

To what power

- 3

should be raised to get

- 2187 ?

EASY

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

Find the value of '

a

' from the following

{(\sqrt{9})}^{- 5} \times {(\sqrt{3})}^{- 7} = {(\sqrt{3})}^{- a}

MEDIUM

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

Find the value of

{[{(\frac{2}{3})}^{2}]}^{2}

EASY

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

Simplify

{(- 3)}^{5} \div {(- 3)}^{2}

HARD

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

Consider the sequence

1, 7, 8, 49, 50, 56, 57, 343, . . . . . . . . .

which consists of sums of distinct powers of

7

that is

7^{0}, 7^{1}, 7^{0} + 7^{1}, 7^{2}, . . . . . . .

in increasing order. At what position will

16856

occurs in this sequence?

HARD

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

In base

- 2

notation, digits are

0

and

1

only and the places go up in powers of

- 2

. For example,

11011

stands for

{(- 2)}^{4} + {(- 2)}^{3} + {(- 2)}^{1} + {(- 2)}^{0}

and equals number

7

in base

10

. If the decimal number

2019

is expressed in base

- 2

, how many non-zero digits does it contain?

HARD

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

If

x^{2 a} = y^{2 b} = z^{2 c} \neq 0

and

x^{2} = y z

, then value of

\frac{a b + b c + c a}{b c}

is:

MEDIUM

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

What is the remainder when we divide

5^{70} + 7^{70}

by

74

?

EASY

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

What is the sum of exponents of prime factors in the prime factorization of

98

?

MEDIUM

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

2^{3} + 2^{3} + 2^{3} + 2^{3}

is equal to _____

MEDIUM

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

If

3^{x} = 6561,

then

3^{x - 3} =

MEDIUM

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

The value of

a^{b} - b^{a},

if

a = 3

and

b = 7

is _____.

MEDIUM

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

Select the CORRECT match.

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Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

Write the following in exponential form.

y \times y \times z \times z \times z \times m \times m

MEDIUM

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

If

2^{n} = 1024,

then

2^{(\frac{n}{2} + 2)} =

EASY

Mathematics>Arithmetic>Exponents and Powers>Basics of Exponents

Express

10000

as a product of prime factors.