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Maths Solve The Following Question.1MARKS

Exponents · Maharashtra Board STD 8 (MSBSHSE - Semi English Medium). 33 questions.

Questions

Solve The Following Question.1MARKS

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33 questions · self-marked practice — reveal the answer and mark yourself.

Question 11 Mark
Evaluate:
$\Big(\frac{5}{6}\Big)^{6}\times\Big(\frac{5}{6}\Big)^{-4}$
Answer
$\Big(\frac{5}{6}\Big)^{6}\times\Big(\frac{5}{6}\Big)^{-4}$
$=\Big(\frac{5}{6}\Big)^{6-4}$
$=\Big(\frac{5}{6}\Big)^{2}$
$=\frac{5}{6}\times\frac{5}{6}$
$=\frac{25}{36}$
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Question 21 Mark
Write the following numbers in usual form:
$3.74\times10^5$
Answer
$3.74\times10^5$
$=\frac{374}{100}\times10^5$
$=\frac{374}{10^2}\times10^5$
$=374\times1000$
$=374000$
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Question 31 Mark
Evaluate:
$\Big(\frac{-2}{3}\Big)^{-5}$
Answer
$\Big(\frac{-2}{3}\Big)^{-5}=\Big(\frac{-3}{2}\Big)^{5}$
$=\Big(\frac{-3}{2}\Big)\times\Big(\frac{-3}{2}\Big)\times\Big(\frac{-3}{2}\Big)\times\Big(\frac{-3}{2}\Big)\times\Big(\frac{-3}{2}\Big)$
$=\frac{-243}{32}$
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Question 41 Mark
Fill in the blank.$\Big(\frac{-2}{3}\Big)^{-2}=\ ......$
Answer
$\Big(\frac{-2}{3}\Big)^{-2}=\frac{9}{4}$Solution:
$\Big(\frac{-2}{3}\Big)^{-2}$
$=\Big(\frac{3}{-2}\Big)^{2}$
$=\frac{3^2}{-2^2}$
$=\frac{9}{4}$
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Question 51 Mark
Evaluate:
$\Big(\frac{-2}{3}\Big)^{-5}$
Answer
$\Big(\frac{-2}{3}\Big)^{-5}$
$=\Big(\frac{3}{-2}\Big)^{5}$
$=\frac{3^{5}}{-2^{5}}$
$=\frac{243}{-32}$
$=\frac{243\times-1}{-32\times-1}$
$=\frac{-243}{32}$
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Question 61 Mark
Fill in the blank.
$5.32 \times 10^{-4}$ in usual form is ________.
Answer
$5.32 \times 10^{-4}$ in usual form is 0.00532.

$5.32\times10^{-4}$

$=\frac{5.32}{10^4}$

$=\frac{5.32}{10000}$

$=0.000532$
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Question 81 Mark
Write the following numbers in standard form:
$4630000000000$
Answer
$4630000000000$
$=4.63 \times 10^{12}$
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Question 91 Mark
Evaluate:
$\Big(\frac{1}{2}\Big)^{-5}$
Answer
$\Big(\frac{1}{2}\Big)^{-5}$

$=(2)^5=2\times2\times2\times2\times2$

$=32$
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Question 101 Mark
Fill in the blank.0.0000123 written in standard form is __________.
Answer
0.0000123 written in standard form is $1 . 2 3 \times 10^{-5}$.

$0.0000123$

$=\frac{123}{10000000}$

$=\frac{123}{10^7}$

$=\frac{1.23\times100}{10^7}$

$=\frac{1.23\times10^2}{10^7}$

$=1.23\times10^{(2-7)}$

$=1.23\times10^{-5}$
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Question 111 Mark
Evaluate:
$\Big(\frac{9}{8}\Big)^{-3}\times\Big(\frac{9}{8}\Big)^{2}$
Answer
$\Big(\frac{9}{8}\Big)^{-3}\times\Big(\frac{9}{8}\Big)^{2}$ $=\Big(\frac{9}{8}\Big)^{-3+2}$ $=\Big(\frac{9}{8}\Big)^{-1}$$=\frac{8}{9}$
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Question 121 Mark
Evaluate:
$\Big(\frac{5}{7}\Big)^{0}$
Answer
$\Big(\frac{5}{7}\Big)^{0}$Using the property $\Big(\frac{\text{a}}{\text{b}}\Big)^0=1$
We, have:
$\Big(\frac{5}{7}\Big)^{0}=1$
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Question 131 Mark
Write the following numbers in standard form:
$345 \times 10^5$
Answer
$345 \times 10^5$
$=3.45 \times 10^2 \times 10^5$
$=3.45 \times 10^7$
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Question 141 Mark
The height of Mount Everest is 8848m. Write it in standard form.
Answer
Height of Mount Everest $=8848 m$
$=8.848 \times 1000$
$=8.848 \times 10^3$ ​​​​​​​
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Question 151 Mark
The distance from the earth to the sun is 149600000000m. Write it in standard form.
Answer
Distance between the earth and the sun $=149600000000 m$

$=(1.49600000000 \times 100000000000) m$

$=\left(1.496 \times 10^{11}\right) m$
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Question 161 Mark
Evaluate:
$\Big(\frac{5}{3}\Big)^{2}\times\Big(\frac{5}{3}\Big)^{2}$
Answer
$\Big(\frac{5}{3}\Big)^{2}\times\Big(\frac{5}{3}\Big)^{2}$
$=\Big(\frac{5}{3}\Big)^{2+2}$
$=\Big(\frac{5}{3}\Big)^{4}$
$=\frac{5}{3}\times\frac{5}{3}\times\frac{5}{3}\times\frac{5}{3}$
$=\frac{625}{81}$
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Question 171 Mark
Fill in the blank.
Fill in the blank. $3 \times 10^{-3}$ in usual form is ________.
Answer
$3 \times 10^{-3}$ in usual form is $\underline{0.003}$.

$3\times10^{-3}$

$=\frac{3}{10^3}$

$=\frac{3}{1000}$

$=0.003$
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Question 181 Mark
Mark $(\checkmark)$ against the correct answer of the following:
If $\Big(\frac{5}{12}\Big)^{-4}\times\Big(\frac{5}{12}\Big)^{3\text{x}}=\Big(\frac{5}{12}\Big)^5$, then x = ?
  1. -1
  2. 1
  3. 2
  4. 3
Answer
  1. 3
Solution:

$\Big(\frac{5}{12}\Big)^{-4}\times\Big(\frac{5}{12}\Big)^{3\text{x}}=\Big(\frac{5}{12}\Big)^5$

$\Rightarrow\Big(\frac{5}{12}\Big)^{-4+3\text{x}}=\Big(\frac{5}{12}\Big)^5$

$\Rightarrow-4+3\text{x}=5$

$\Rightarrow3\text{x}=5+4=9$

$\Rightarrow\text{x}=\frac{9}{3}$

$\Rightarrow\text{x}=3$
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Question 201 Mark
Evaluate:
$4^{-3}$
Answer
$4^{-3}=\Big(\frac{1}{4}\Big)^3$

$=\frac{1}{4}\times\frac{1}{4}\times\frac{1}{4}$

$=\frac{1}{64}$
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Question 211 Mark
Express the following in standard form:0.000003
Answer
$0.000003$$​​=\frac{3}{1000000}$
$=3\times10^{-6}$
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Question 231 Mark
Evaluate:
$\Big(\frac{3}{4}\Big)^{-2}$
Answer
$\Big(\frac{3}{4}\Big)^{-2}$
$=\Big(\frac{4}{3}\Big)^{2}$
$=\Big(\frac{4^2}{3^2}\Big)$
$=\frac{16}{9}$
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Question 241 Mark
Evaluate:
$\Big(\frac{2}{3}\Big)^{-3}\times\Big(\frac{2}{3}\Big)^{-2}$
Answer
$\Big(\frac{2}{3}\Big)^{-3}\times\Big(\frac{2}{3}\Big)^{-2}$
$=\Big(\frac{3}{2}\Big)^{3}\times\Big(\frac{3}{2}\Big)^{2}$
$=\Big(\frac{3}{2}\Big)^{3+2}$
$=\Big(\frac{3}{2}\Big)^{5}$
$=\frac{3}{2}\times\frac{3}{2}\times\frac{3}{2}\times\frac{3}{2}\times\frac{3}{2}$
$=\frac{243}{32}$
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Question 271 Mark
Fill in the blank.
360000 written in standard form is _________.
Answer
360000 written in standard form is $3.6 \times 10^5$.

$360000=3.6 \times 10^4$

$=3.6 \times 10 \times 10^4$

$=3.6 \times 10^{(1+4)}$

$=3.6 \times 10^5$
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Question 281 Mark
Tick $(\checkmark)$ the correct answer the following:
$\Bigg[\bigg\{\Big(-\frac{1}{2}\Big)^2\bigg\}^{-2}\Bigg]=\ ?$
  1. $\frac{1}{16}$
  2. $16$
  3. $-\frac{1}{16}$
  4. $-16$
Answer
  1. $\frac{1}{16}$
Solution:

$\Bigg[\bigg\{\Big(-\frac{1}{2}\Big)^2\bigg\}^{-2}\Bigg]$

$=\Big(\frac{-1}{2}\Big)^{2\times(-2)(-1)}$

$=\Big(\frac{-1}{2}\Big)^4$

$=\Big(\frac{-1}{2}\Big)\Big(\frac{-1}{2}\Big)\Big(\frac{-1}{2}\Big)\Big(\frac{-1}{2}\Big)$

$=\frac{1}{16}$
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Question 311 Mark
Evaluate:
$\Big(\frac{4}{3}\Big)^{-3}$
Answer
$\Big(\frac{4}{3}\Big)^{-3}$
$=\Big(\frac{3}{4}\Big)^{3}$
$=\frac{3}{4}\times\frac{3}{4}\times\frac{3}{4}$
$=\frac{27}{64}$
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Question 321 Mark
The speed of light is 300000000m/ sec. Express it in standard form.
Answer
Speed of Light $=300000000 m / sec$
$=3.00000000 \times 100000000$
$=\left(3 \times 10^8\right) m / sec$
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Question 331 Mark
Evaluate:
$(-3)^{-4}$
Answer
$(-3)^{-4}=\Big(\frac{1}{-3}\Big)^{4}$
$=\Big(\frac{-1}{3}\Big)\times\Big(\frac{-1}{3}\Big)\times\Big(\frac{-1}{3}\Big)\times\Big(\frac{-1}{3}\Big)$
$=\frac{1}{81}$
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