These NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers InText Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers InText Questions

NCERT Intext Question Page No. 194

Question 1.

Find the multiplicative inverse of the following:

(i) 2^{-4}

(ii) 10^{5}

(iii) 7^{-2}

(iv) 5^{-3}

(v) 10^{-100}

Answer:

(i) The multiplicative inverse of 2^{-4} = 2^{4}

(ii) The multiplicative inverse of 10^{-5} = 10^{5}

(iii) The multiplicative inverse of 7^{-2} = 7^{2}

(iv) The multiplicative inverse of 5^{-3} = 5^{3}

(v) The multiplicative inverse of 10^{-100} = 10^{100}

Question 2.

Expand the following numbers using exponents.

(i) 1025.63

(ii) 1256.249

Answer:

Number | Expanded form |

(i) 1025.63 | 1 x 1000 + 0 x 100 + 2 x 10 + 5 x 1 \(\frac{6}{10}+\frac{3}{100}\) or 1 x 10 ^{3} + 2 x 10^{1} + 5 x 10° + 6 x 10^{-1} + 3 x 10^{-2} |

(ii) 1025.249 | 1 x 1000 +2 x 100 +5 x 10 + 6 x 1 + \(\frac{2}{10}+\frac{4}{100}+\frac{9}{1000}\) or 1 x 10 ^{3} + 2 x 10^{2} + 5 x 10^{1} + 6 x 10° + 2 x 10^{-1} + 9 x 10^{-3} |

NCERT Intext Question Page No. 195

Question 1.

Simplify and write in exponential form.

(i) (-2)^{-3} x (-2)^{-4}

(ii) p^{3} x p^{-10}

(iii) 3^{2} x 3^{-5} x 3^{6}

Answer:

(i) (-2)^{-3} x (-2)^{-4} = (-2)^{3-4}

[a^{m} x a^{n} = a^{m+n}]

= (-2)^{-7} = \(\frac{1}{(-2)^{7}}\)

(ii) p^{3} x p^{-10} = p^{3 + (-10)} = p^{3 – 10 }= p^{7} or \(\frac{1}{\mathrm{p}^{7}}\)

(iii) 3^{2} x 3^{-5} x 3^{6} = 3^{2 + (- 5) + 6} = 3^{2 – 5 + 6} = 3^{8-5} = 3^{3}

NCERT Intext Question Page No. 199

Question 1.

Write the following numbers in standard form.

(i) 0.000000564

(ii) 0.0000021

(iii) 15240000

Answer:

(i) 0.000000564 = \(\frac{564}{1000000000}=\frac{564}{10^{9}}\)

= \(\frac{5.64 \times 10^{2}}{10^{9}}\) = 5.64 x 10^{-7}

(ii) 0.0000021 = \(\frac{21}{10000000}=\frac{21}{10^{7}}\)

= \(\frac{2.1 \times 10}{10^{7}}\) = 2.1 x 10^{1-7} = 2.1 x 10^{-6}

(iii) 15240000 = 1524 x 10000

= 1.524 x 1000 x 10000 = 1.524 x 10^{7}

∴ 15240000 = 1.524 x 10^{7}

Question 2.

Write all the facts give in the standard form.

Answer:

A number is said to be in the standard form when it is written as k x 10^{n}, Where 1 ≤ k < 10 and ‘n’ is an integer. A number expressed as the product of a number between 1 and 10 and an integral power of 10.

Example: Compare the size of a red blood cell which is 0.000007m to that of a plant cell which is 0.0000129m.

Size of red blood cell = 0.000007 m

= \(\frac{7}{1000000}\) x 10^{-6} m

Size of the plant cell = \(\frac{7}{10000000} \mathrm{~m}=\frac{1.29 \times 10^{2}}{10000000} \mathrm{~m}\)

= 1.29 x 10^{-5} m

Now = \(\frac{7 \times 10^{-6}}{1.29 \times 10^{-5}}=\frac{7 \times 10^{-1}}{1.29}\)

= \(\frac{7 \times 10^{-1}}{1.3}=\frac{0.7}{1.3}=\frac{1}{2}\) (approx)

Thus, the size of a red blood cell is half of the plant cell size.