Find the unknown value in the following number. 4 . 86856 × 10 c = 486856

We need to find the value of c in 4 . 86856 × 10 c = 486856 . LHS = 4 .86856 × 10 c ..... i RHS = 486856 Now, we will convert 486856 in standard exponential form. We know that, A number is in standard form when it is written as a × 10 n , where a is a decimal number greater than or equal to 1 and less than 10 and n is a positive integer. Thus, 486856 = 4 .86856 × 100000 = 4 .86856 × 10 5 Thus, RHS = 486856 = 4 .86856 × 10 5 ... ii By comparing i and ii , we have 4 .86856 × 10 c = 4 .86856 × 10 5 ⇒ 10 c = 10 5 ⇒ c = 5 ∵ If a n = a m then m = n Hence, the unknown value in the given number is 5 .

Write the following in exponential form. 5 × 5 × 2 × a × a × a

Given expression as, 5 × 5 × 2 × a × a × a Here we can see 5 is multiplied by itself 2 times, 2 is multiplied by itself 1 times and a is multiplied by itself 3 times. So, we can write given expression as, 5 × 5 × 2 × a × a × a = 5 2 × 2 1 × a 3 Where 5 , 2 and a are base and 2 , 1 and 3 are their exponents. Hence, the exponential form of 5 × 5 × 2 × a × a × a = 5 2 × 2 1 × a 3 .

Find the unknown value in the following number. 7.65758 × 10 f = 765758

We need to find the value of f in 7 .65758 × 10 f = 765758 . LHS = 7 .65758 × 10 f ..... i RHS = 765758 Now, we will convert 765758 in standard exponential form. We know that, A number is in standard form when it is written as a × 10 n , where a is a decimal number greater than or equal to 1 and less than 10 and n is a positive integer. Thus, 765758 = 7 . 65758 × 100000 = 7 . 65758 × 10 5 Thus, RHS = 765758 = 7 . 65758 × 10 5 ... ii By comparing i and ii , we have = 7 . 65758 × 10 f = 7 . 65758 × 10 5 ⇒ 10 f = 10 5 ⇒ f = 5 ∵ If a n = a m then m = n Hence, the unknown value is 5 .

Find the unknown value in the following number. 2.8748 × 10 a = 28748

We need to find the value of a in 2.8748 × 10 a = 28748 . LHS = 2 . 8748 × 10 a ..... i RHS = 28748 Now, we will convert 28748 in standard exponential form. We know that, A number is in standard form when it is written as a × 10 n , where a is a decimal number greater than or equal to 1 and less than 10 and n is a positive integer. Thus, 28748 = 2 . 8748 × 10000 = 2 . 8748 × 10 4 Thus, RHS = 28748 = 2 . 8748 × 10 4 ... ii By comparing i and ii , we have 2 . 8748 × 10 a = 2 . 8748 × 10 4 ⇒ 10 a = 10 4 ⇒ a = 4 ∵ if a n = a m then m = n Hence, the unknown value is 4 .

Write the following in exponential form. m × m × m × m × m

Given expression is, m × m × m × m × m Here we can see m is multiplied five times by itself. So, we can write it as m × m × m × m × m = m 5 It is read as m to the power 5 . Here, m is the base and 5 is the exponent. Hence, the exponential form of m × m × m × m × m is m 5 .

Find the unknown value in the following number. 7 . 0241 × 10 d = 70241

We need to find the value of d in 7 . 0241 × 10 d = 70241 . LHS = 7 . 0241 × 10 d ..... i RHS = 70241 Now, we will convert 70241 in standard exponential form. We know that, A number is in standard form when it is written as a × 10 n , where a is a decimal number greater than or equal to 1 and less than 10 and n is a positive integer. Thus, 70241 = 7 . 0241 × 10000 = 7 . 0241 × 10 4 Thus, RHS = 70241 = 7 . 0241 × 10 4 ... ii By comparing i and ii , we have = 7 . 0241 × 10 d = 7 . 0241 × 10 4 ⇒ 10 d = 10 4 ⇒ d = 4 ∵ if a n = a m then m = n Hence, the unknown value is 4 .

Find the unknown value in the following number. 6 . 5865 × 10 e = 65865

We need to find the value of e in 6 . 5865 × 10 e = 65865 . LHS = 6 . 5865 × 10 e ..... i RHS = 65865 Now, we will convert 65865 in standard exponential form. We know that, A number is in standard form when it is written as a × 10 n , where a is a decimal number greater than or equal to 1 and less than 10 and n is a positive integer. Thus, 65865 = 6 . 5865 × 10000 = 6 . 5865 × 10 4 Thus, RHS = 65865 = 6 . 5865 × 10 4 ... ii By comparing i and ii , we have 6 . 5865 × 10 e = 6 . 5865 × 10 4 ⇒ 10 e = 10 4 ⇒ e = 4 ∵ If 4 6 = 4 x then x = 6 Hence, the unknown value is 4 .

E M B I B E

Mathematics>Algebra>Exponents>Basics of Exponents

EASY

Earn 100

The Volume of sphere (V) is 972$ \pi $$ \text{c}{\text{m}}^{3}$.
The formula to find the volume V = $ \frac{4}{3}$$ \pi {r}^{3}$, where $ r$ is the radius of the sphere.
The radius of the sphere is cm.

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Important Questions on Exponents

HARD

Mathematics>Algebra>Exponents>Basics of Exponents

Find the largest value of

a^{b}

such that the positive integers

a, b > 1

satisfy

a^{b} b^{a} + a^{b} + b^{a} = 5329

.

EASY

Mathematics>Algebra>Exponents>Basics of Exponents

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

98

?

MEDIUM

Mathematics>Algebra>Exponents>Basics of Exponents

The number of digits in the decimal expansion of

16^{5} 5^{16}

is

EASY

Mathematics>Algebra>Exponents>Basics of Exponents

Express the following as the product of powers of their prime factors.

1, 024

MEDIUM

Mathematics>Algebra>Exponents>Basics of Exponents

Find the unknown value in the following number.

4.86856 \times 10^{c} = 486856

MEDIUM

Mathematics>Algebra>Exponents>Basics of Exponents

Select the CORRECT match.

MEDIUM

Mathematics>Algebra>Exponents>Basics of Exponents

Write the following in exponential form.

$5 \times 5 \times 2 \times a \times a \times a$

EASY

Mathematics>Algebra>Exponents>Basics of Exponents

Express the following as the product of powers of their prime factors.

675

MEDIUM

Mathematics>Algebra>Exponents>Basics of Exponents

$2^{3^{2}} =$

EASY

Mathematics>Algebra>Exponents>Basics of Exponents

Calculate the value of

{(- 1)}^{100}

.

MEDIUM

Mathematics>Algebra>Exponents>Basics of Exponents

Find the unknown value in the following number.

7.65758 \times 10^{f} = 765758

MEDIUM

Mathematics>Algebra>Exponents>Basics of Exponents

Find the unknown value in the following number.

2.8748 \times 10^{a} = 28748

MEDIUM

Mathematics>Algebra>Exponents>Basics of Exponents

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

is equal to _____

EASY

Mathematics>Algebra>Exponents>Basics of Exponents

Express the following as the product of powers of their prime factors.

324

MEDIUM

Mathematics>Algebra>Exponents>Basics of Exponents

Write the following in exponential form.

$m \times m \times m \times m \times m$

EASY

Mathematics>Algebra>Exponents>Basics of Exponents

If the exponential form of $a \times a \times a \times b \times b \times b \times b \times c \times c \times c = a^{x} b^{y} c^{z}$ , then find the value of $x + y + z$ .