Ncert solutions mathematics class 8 Solutions for Chapter 12 exponents and powers

Q1) Evaluate.

(i) 3^{-2}

(ii) \left(-4\right)^{^{-2}}

(iii) \left(\frac{1}{5}\right)^{-5}

Evaluate:

\text { (i) } 3^{-2} (i i)(-4)^{-2} \left(\frac{1}{2}\right)^{-5}

Evaluate:

\frac{8^{-1} \times 5^{8}}{2^{-4}}

Simplify and express the result in power notation with positive exponent:

\text { (i) }(-4)^{5} \div(-4)^{8}

\text { (ii) }\left(\frac{1}{2^{3}}\right)^{2}

\text { (iii) }-(3)^{4} \times\left(\frac{5}{3}\right)^{4}

\text { (iv) }\left(3^{-7} \div 3^{-10}\right) \times 3^{-5}

\text { (v) } 2^{-3} \times(-7)^{-3}

\begin{aligned} &\text { v) } 2^{-3} \times(-7)^{-3}\\ &=(2 \times-7)^{-3}\\ &\text { (Because } \left.a^{\wedge} m \times b^{\wedge} m=(a b)^{\prime} m\right)\\ &=1 /(2 \times-7)^{3}\\ &\left[\because a^{-n}=\frac{1}{a^{m}}\right]\\ &=1 /(-14)^{3} \end{aligned}

Q2) Simplify and express the result in power notation with positive exponent.

(i) \left(-4\right)^5\ \div\ \left(-4\right)^8

(ii) \left(\frac{1}{2^3}\right)^2

(iii) \left(-3\right)^4\ \times\left(\frac{5}{3}\right)^4

(iv) \left(3^{-7}\ \div\ 3^{-10}\right)\ \times3^{-5}

(v) 2^{-3}\times\left(-7\right)^{-3}

Q3) Find the value of:

(i)\left(3^0+4^{-1}\right)\times2^2

(ii) \left(2^{-1}\times\ 4^{-1}\right)\div2^{-2}

(iii) \left(\frac{1}{2}\right)^{-2}+\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{4}\right)^{-2}

(iv) \left(3^{-1}+4^{-1}+5^{-1}\right)^0

(v) \left\{\left(-\frac{2}{3}\right)^{-2}\right\}^2

Find the value of :

\text { (i) }\left(3^{0}+4^{-1}\right) \times 2^{2}

Evaluate:

\text { (iii) }\left(\frac{1}{2}\right)^{-2}+\left(\frac{1}{3}\right)^{-2}+\left(\frac{1}{4}\right)^{-2}

Find the value of :

\text { (ii) }\left(2^{-1} \times 4^{-1}\right) \div 2^{-2}

Evaluate:

\left\{\left(-\frac{2}{3}\right)^{-2}\right\}^{2}

Evaluate:

\left(3^{-1}+4^{-1}+5^{-1}\right)^{0}

Evaluate:

\left(5^{-1} \times 2^{-1}\right) \times 6^{-1}

Q4) Evaluate:

(i) \frac{8^{-1}\times5^3}{2^{-4}}

(ii) \left(5^{-1}\times2^{-1}\right)\times6^{-1}

Q5) Find the value of m for which

.5^m\div5^{-3}=5^5

\text { Find the value of } m \text { for which } 5 \text { m } \div 5^{3}=5^{5}

Q6) Evaluate:

(i) \left\{\left(\frac{1}{3}\right)^{-1}-\left(\frac{1}{4}\right)^{-1}\right\}^{-1}

(ii) \left(\frac{5}{8}\right)^{-7}\times\left(\frac{8}{5}\right)^{-4}

Simplify:

\frac{3^{-5} \times 10^{-5} \times 125}{5^{-7} \times 6^{-5}}

Simplify:

\frac{25 \times t^{-4}}{5^{-2} \times 10 \times t^{-8}}(t \neq 0)

Q7) Simplify.

(i) \frac{25\times t^{-4}}{5^{-3}\times10\times t^{-8}}\ \ \ \left(t\ \ne0\right)

(ii) \frac{3^{-5}\times10^{-5}\times125}{5^{-7}\times6^{-5}}

Q1) Express the following numbers in standard form.

(i) 0.0000000000085

(ii) 0.00000000000942

(iii) 6020000000000000

(iv) 0.00000000837

(v) 31860000000

Express the following numbers in standard form.

(i) 0.0000000000085

(ii) 0.00000000000942

(iii) 6020000000000000

(iv) 0.00000000837

(v) 31860000000

Express the following numbers in the usual form:

Q2) Express the following numbers in usual form.

(i) 3.02 ×10^{-6}

(ii) 4.5 × 10^4

(iii) 3 ×10^{-8}

(iv) 1.0001 ×10^9

(v) 5.8 ×10^{12}

(vi) 3.61492 × 10^6

Q3) Express the number appearing in the following statements in standard form.

(i) 1 micron is equal to 11000000 m.

(ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb.

(iii) Size of a bacteria is 0.0000005 m

(iv) Size of a plant cell is 0.00001275 m

(v) Thickness of a thick paper is 0.07 mm

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

(i) 1 micron is equal to 1/1000000 m.

(ii) Charge of an electron is 0.000, 000, 000, 000, 000, 000, 16 coulomb.

(iii) Size of bacteria is 0.0000005 m

(iv) Size of a plant cell is 0.00001275 m

(v) Thickness of a thick paper is 0.07 mm

Q4) In a stack there are 5 books each of thickness 20mm and 5 paper sheets each of

thickness 0.016 mm. What is the total thickness of the stack.

In a stack, there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm.

What is the total thickness of the stack?