M l aggarwal understanding icse mathematics class 8 Solutions for Chapter 2 exponents and powers

Evaluate:

(i) (3/5)-2

(ii) (-3)-3

(iii) (2/7)-4

Simplify

(i) [(2)-1 + (4)-1 + (3)-1]-1

(ii) [(4)-1 – (5)-1]2 × (5/8)-1

(iii) [40 + 42 – 23] × 3-2

(iv) [(5)2 – (1/4)-2] × (3/4)-2

Find the multiplicative inverse of the following:

(i) (81/16)-3/4

(ii) {(-3/2)-4}1/2

(iii) (5/7)-2 × (5/7)4 ÷ (5/7)3

(i) Express 16-2 as a power with base 2.

(ii) Express 125-4 as a power with base 5.

Write the following numbers in expanded form using exponents:

(i) 2789.453

(ii) 3007.805

Simplify and write in exponential form with positive exponent:

(i)\left[\left\{(5 / 7)^{2}\right\}^{-1}\right]^{-3}

(ii) (2 / 7)^{2} \times(7 / 2)^{-3} \div\left\{(7 / 5)^{-2}\right\}^{-4}

(iii)(4 / 5)^{2} \times 5^{4} \times(2 / 5)^{-2} \div(5 / 2)^{-3}

(iv)\left[8^{-1 \times 5}\right] / 2^{-4}

Simplify and write the following in exponential form:

\text { (i) }\left((-2)^{3}\right)^{2}+5^{-3} \div 5^{-5}-(-1 / 2)^{0}

\text { (ii) } 3^{-3} \times 3^{2} \div 3^{-0}+\left(2^{2} \times 3\right)^{2}+(2 / 3)^{-1}+2^{-1}+(1 / 19)^{-1}

Simplify and write in exponential form with negative exponent:

(i)(i) 5^{3} \times(4 / 5)^{3} (ii) \left((3 / 7)^{-2}\right]^{-3}(iii) (5 / 9)^{-2} \times(5 / 3)^{2} \div(1 / 5)^{-2} ( iv ) 2^{-1}\left[(5 / 3)^{4}+(3 / 5)^{-2}\right] \div(17 / 9)

(v)(-7)^{3} \times(1 /-7)^{-9} \div(-7)^{10}

Simplify:

\text { (i) }\left(49 \times \mathrm{z}^{-3}\right) /\left(7^{-3} \times 10 \times \mathrm{z}^{-5}\right)(\mathrm{z} \neq 0)

\text { (ii) }\left(9^{3} \times 27 \times t^{4}\right) /\left(3^{2} \times 3^{4} \times t^{2}\right)

\left[\left(3^{-2}\right)^{2} \times\left(5^{2}\right)^{-3} \times\left(-t^{-3}\right)^{2}\right] /\left[\left(3^{-2}\right)^{5} \times\left(5^{3}\right)^{-2} \times\left(t^{-4}\right)^{3}\right]

\text { (iv) }\left(2^{-5} \times 15^{-5} \times 500\right) /\left(5^{-6} \times 6^{-5}\right)

By what number should (3/-2)-3 be divided to get (2/3)2?

Find the value of m for which9^{m} \div 3^{-2}=9^{4}

\text { If }(-5 / 7)^{-4} \times(-5 / 7)^{12}=\left\{(-5 / 7)^{3}\right\} \times(-5 / 7)^{-1}, \text {find the value of } x

\text { Find } \mathrm{x}, \text { if }(-2 / 3)^{-13} \times(3 /-2)^{8}=(-2 / 3)^{-2 \mathrm{x}+1}

(i) If 52x-1 = 1/(125) x-3, find x.

(ii) If (9n × 35 × 273)/(3×814) = 27, find n.

Express the following numbers in standard form:

(i) 0.0000000000085

(ii) 0.000000000000942

(iii) 6020000000000000

(iv) 0.00000000837

Express the following numbers in the usual form

\text { (i) } 3.02 \times 10^{-6}

\text { (ii) } 1-007 \times 10^{11}

\text { (iii) } 5.375 \times 10^{14}

\text { (iv) } 7.579 \times 10^{-14}

Express the number appearing in the following statements in standard form:

(i) The mass of a proton is 0.000000000000000000000001673 gram.

(ii) The thickness of a piece of paper is 0.0016 cm.

(iii) The diameter of a wire on a computer chip is 0.000003 m.

(iv) A helium atom has a diameter of 22/100000000000 m.

(v) The mass of a molecule of hydrogen gas is about 0.00000000000000000000334 tons.

(vi) The human body has 1 trillion cells which vary in shapes and sizes.

(vii) The distance from the Earth of the Sun is 149,600,000,000 m.

(viii) The speed of light is 300,000,000 m/sec.

(ix) Mass of the Earth is 5,970,000,000,000,000,000,000,000 kg.

(x) Express 3 years in seconds.

(xi) Express 7 hectares in cm2.

(xii) A sugar factory has annual sales of 3 billion 720 million kilograms of sugar.

Compare the following:

(i) Size of a plant cell to the thickness of a piece of paper.

(ii) Size of a plant cell to the diameter of a wire on a computer chip.

(iii) The thickness of a piece of paper to the diameter of a wire on a computer chip.

Given the size of plant cell = 0.00001275 m

The thickness of a piece of paper = 0.0016 cm

The diameter of a wire on a computer chip = 0.000003 m

The number of red blood cells per cubic millimeter of blood is approximately 5.5

million. If the average body contains 5 liters of blood, what is the total number of

red cells in the body? (1 liter = 1,00,000 mm3)

Mass of Mars is 6.42 × 1029 kg and the mass of the sun is 1.99 × 10^{30} \mathrm{kg} What is

the total mass?

A particular star is at a distance of about 8.1 ×10^{13}km from the Earth. Assuming

that the light travels at 3 × 108 m/sec, find how long does light take from that star to

reach the Earth.