Exponents And P...

Find the value of .

Simplify: (x^-2 + y^-2)^-2

The value of y + 2y(y^2y) at y = 2 is

Which of the following options is the simplified form of the given expression?

If , find the value of x.

_{Find the value of the expression} .

_{If , find the value of} .

If × 3^x - 3^{(x - 2)} = 243, find the value of x.

Which of the following values are equal?

A) 1^-1
B) 5⁰
C) 0¹
D) 1¹

Find the value of (4^-1 - 7^-1)^-1 - (4^-1 - 3^-1)^-1.

After expressing 7 × 10^-4 - 4000 × 10^-3 in standard form, we will get

If 2^{(x - y)} = 64 and 2^{(x + y)} = 256, find the value of x.

The number of prime factors in 6¹⁰ × 7¹⁷ × 55²⁷ is

If , find the value of x.

The population of England is 5.11 × 10⁷ and that of Northern Ireland is 1.82 × 10⁶. What is the difference between the populations, in standard form?

The distance between Mercury and Mars is approximately 2,05,00,00,000 miles. How can this distance be represented in standard index form?

Rameshwari is a scientist. She is working on an experiment about atom. An atom is made up of protons, electrons, neutrons and nucleus. She finds out that the weight of a proton in the atom of an element is 0.00001275 on the carbon-12 scale. Express the weight of a proton in standard form.

The height of World Trade Centre is 4.696 × 10⁵ mm. What will be its height when written in usual form?

The mass of the Sun is approximately 2 × 10³⁰ kg and the mass of the Earth is 6 × 10²⁴ kg. What is the sum of both the masses?

If 6^x + 6^{x - 1} = 42, then 2^{x - 1} equals

What is the value of ?

Fill in the blanks:

(i) The value of 32^(0.16) × 32^(0.04) is P .

(ii) If 7⁵ × 28⁴ = 4⁴ × 7ⁿ, then n = Q .

(iii) The value of is R .

Match the expressions given in Column I with their correct answers in Column II.

If X = , Y = and Z = , find the values of the following expressions:

(i) x² + y² + z²
(ii) 5xyz