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Question 511 Mark

Express the following numbers in standard form:
82934000000

Answer

We can write in standard form
$82934000000=8.2934000000 \times 10^{10}$
$=8.2934 \times 10^{10}$

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Question 521 Mark

Write the reciprocal of: $\Big(\frac{2}{3}\Big)^4$

Answer

We know that the reciprocal of $\Big(\frac{\text{a}}{\text{b}}\Big)^\text{m}\text{ is }\Big(\frac{\text{b}}{\text{a}}\Big)^\text{m}$ Reciprocal of $\Big(\frac{2}{3}\Big)^4=\Big(\frac{3}{2}\Big)^4$

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Question 531 Mark

Write the reciprocal of: $\Big(\frac{-3}{5}\Big)^{61}$

Answer

We know that the reciprocal of $\Big(\frac{\text{a}}{\text{b}}\Big)^\text{m}\text{ is }\Big(\frac{\text{b}}{\text{a}}\Big)^\text{m}$ Reciprocal of $\Big(\frac{-3}{5}\Big)^{61}=\Big(\frac{-5}{3}\Big)^{61}$

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Question 541 Mark

Write the reciprocal of:
$\Big(\frac{-3}{5}\Big)^{61}$

Answer

We know that the reciprocal of $\Big(\frac{\text{a}}{\text{b}}\Big)^\text{m}\text{ is }\Big(\frac{\text{b}}{\text{a}}\Big)^\text{m}$
Reciprocal of $\Big(\frac{-3}{5}\Big)^{61}=\Big(\frac{-5}{3}\Big)^{61}$

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Question 551 Mark

Write the reciprocal of:
$\Big(\frac{2}{3}\Big)^4$

Answer

We know that the reciprocal of $\Big(\frac{\text{a}}{\text{b}}\Big)^\text{m}\text{ is }\Big(\frac{\text{b}}{\text{a}}\Big)^\text{m}$
Reciprocal of $\Big(\frac{2}{3}\Big)^4=\Big(\frac{3}{2}\Big)^4$

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Question 561 Mark

Write the reciprocal of:
$(-5)^{6}$

Answer

We know that the reciprocal of $\Big(\frac{\text{a}}{\text{b}}\Big)^\text{m}\text{ is }\Big(\frac{\text{b}}{\text{a}}\Big)^\text{m}$
Reciprocal of (-5)⁶ = Reciprocol of $\Big(\frac{-5}{1}\Big)^6=\Big(\frac{-1}{5}\Big)^6$

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Question 571 Mark

Write the reciprocal of:
$2^{5}$

Answer

We know that the reciprocal of $\Big(\frac{\text{a}}{\text{b}}\Big)^\text{m}\text{ is }\Big(\frac{\text{b}}{\text{a}}\Big)^\text{m}$
Reciprocal of 2⁵ = Reciprocol of $\Big(\frac{2}{1}\Big)^5=\Big(\frac{1}{2}\Big)^5$

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Question 581 Mark

Write the numeral whose expanded form is given below:
9 × 10⁶ + 7 × 10⁵ + 0 × 10⁴ + 3 × 10³ + 4 × 10² + 6 × 10¹ + 2 × 10⁰

Answer

9 × 10⁶ + 7 × 10⁵ + 0 × 10⁴ + 3 × 10³ + 4 × 10² + 6 × 10¹ + 2 × 10⁰
= 9000000 + 700000 + 0 + 3000 + 400 + 60 + 2
= 9703462

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Question 591 Mark

Write the numeral whose expanded form is given below:
8 × 10⁵ + 6 × 10⁴ + 4 × 10³ + 2 × 10² + 9 × 10¹ + 6 × 10⁰

Answer

8 × 10⁵ + 6 × 10⁴ + 4 × 10³ + 2 × 10² + 9 × 10¹ + 6 × 10⁰
= 800000 + 60000 + 4000 + 200 + 90 + 6
= 864296

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Question 601 Mark

Write the numeral whose expanded form is given below:
6 × 10⁴ + 3 × 10³ + 0 × 10² + 7 × 10¹ + 8 × 10⁰

Answer

6 × 10⁴ + 3 × 10³ + 0 × 10² + 7 × 10¹ + 8 × 10⁰
= 60000 + 3000 + 0 + 70 + 8
= 63078

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Question 611 Mark

Write the following numbers in expanded form:
684502

Answer

684502 = 6 × 10⁵ + 8 × 10⁴ + 4 × 10³ + 5 × 10² + 0 × 10¹ + 2 × 10⁰

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Question 621 Mark

Write the following numbers in expanded form:
5807294

Answer

5807294 = 5 × 10⁶ + 8 × 10⁵ + 0 × 10⁴ + 7 × 10³ + 2 × 10² + 9 × 10¹ + 4 × 10⁰

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Question 631 Mark

Write the following numbers in expanded form:
50074

Answer

50074 = 5 × 10⁴ + 0 × 10³ + 0 × 10² + 7 × 10¹ + 4 × 10⁰

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Question 641 Mark

Write the following numbers in expanded form:
4007185

Answer

4007185 = 4 × 10⁶ + 0 × 10⁵ + 0 × 10⁴ + 7 × 10³ + 1 × 10² + 8 × 10¹ + 5 × 10⁰

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Question 651 Mark

Write the following in power notation:
$\frac{5}{7}\times \frac{5}{7}\times \frac{5}{7}\times\frac{5}{7}$

Answer

$\frac{5}{7}\times \frac{5}{7}\times \frac{5}{7}\times\frac{5}{7}=\Big(\frac{5}{7}\Big)^4$

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Question 661 Mark

Write the following in power notation:
$\Big(\frac{-4}{3}\Big)\times \Big(\frac{-4}{3}\Big)\times \Big(\frac{-4}{3}\Big)\times \Big(\frac{-4}{3}\Big)\times \Big(\frac{-4}{3}\Big)$

Answer

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

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Question 671 Mark

Write the following in power notation:
$\Big(\frac{-1}{6}\Big)\times\Big(\frac{-1}{6}\Big)\times\Big(\frac{-1}{6}\Big)$

Answer

$\Big(\frac{-1}{6}\Big)\times\Big(\frac{-1}{6}\Big)\times\Big(\frac{-1}{6}\Big)=\Big(\frac{-1}{6}\Big)^3$

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Question 681 Mark

Write the following in power notation:
$(-8)\times (-8)\times (-8)\times (-8)\times (-8)$

Answer

$(-8)\times (-8)\times (-8)\times (-8)\times (-8)=(-8)^5$

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Question 691 Mark

Find the value of the following:
8°

Answer

We know that $\Big(\frac{\text{a}}{\text{b}}\Big)^\circ=1,$ therefore
8° = 1

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Question 701 Mark

Find the value of the following:
6° × 7°

Answer

We know that $\Big(\frac{\text{a}}{\text{b}}\Big)^\circ=1,$ therefore
6° × 7° = 1 × 1 = 1

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Question 711 Mark

Find the value of the following:
4° + 5°

Answer

We know that $\Big(\frac{\text{a}}{\text{b}}\Big)^\circ=1,$ therefore
4° + 5° = 1 + 1 = 2

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Question 721 Mark

Find the value of the following:
(-3)°

Answer

We know that $\Big(\frac{\text{a}}{\text{b}}\Big)^\circ=1,$ therefore
(-3)° = 1

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Question 731 Mark

Find the reciprocal of the following:
$\Big(\frac{-5}{6}\Big)^{11}$

Answer

$\Big(\frac{-5}{6}\Big)^{11}=\Big(\frac{-6}{5}\Big)^{11}$

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Question 741 Mark

Find the reciprocal of the following:
$\Big(\frac{3}{8}\Big)^4$

Answer

$\Big(\frac{3}{8}\Big)^4=\Big(\frac{8}{3}\Big)^4$

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Question 751 Mark

Find the reciprocal of the following:
$6^{7}$

Answer

$6^{7}=\Big(\frac{1}{6}\Big)^7$

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Question 761 Mark

Find the reciprocal of the following:
$(-4)^3$

Answer

$(-4)^3=\Big(\frac{-1}{4}\Big)^3$

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Question 771 Mark

Express the following numbers in standard form:
The present age of universe = 12000000000 years.

Answer

The present age of universe = 12000000000 years
= 1.2000000000 × 10¹⁰ years
= 1.2 × 10¹⁰ years

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Question 781 Mark

Express the following numbers in standard form:
Population of India in March 2001 = 1027000000.

Answer

Population of India in March 2001 = 1027000000
= 1.027000000 × 10⁹
= 1.027 × 10⁹

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Question 791 Mark

Express the following numbers in standard form:
Number of stars in a galaxy = 100000000000.

Answer

Number of stars in a galaxy = 100000000000
= 1.00000000000 × 10¹¹
= 1 × 10¹¹

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Question 801 Mark

Express the following numbers in standard form:
Distance between Earth and Moon = 384000000m.

Answer

Distance between Earth and Moon = 384000000m
= 3.84000000 × 10⁸
= 3.84 × 10⁸

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Question 811 Mark

Express the following numbers in standard form:
Diameter of Earth = 12756000m.

Answer

Diameter of Earth = 12756000m
= 1.2756000 × 10⁷m
= 1.2756 × 10⁷m

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Question 821 Mark

Express the following numbers in standard form:
940000000000

Answer

We can write in standard form
940000000000 = 9.40000000000 × 10¹¹
= 9.4 × 10¹¹

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Question 831 Mark

Express the following numbers in standard form:
82934000000

Answer

We can write in standard form
82934000000 = 8.2934000000 × 10¹⁰
= 8.2934 × 10¹⁰

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Question 841 Mark

Express the following numbers in standard form:
6428000

Answer

We can write in standard form
6428000 = 6.428000 × 10⁶
= 6.428 × 10⁶

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Question 851 Mark

Express the following numbers in standard form:
538

Answer

We can write in standard form
538 = 5.38 × 10²

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Question 861 Mark

Express the following numbers in standard form:
23000000

Answer

We can write in standard form
23000000 = 2.3000000 × 10⁷
= 2.3 × 10⁷

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Question 871 Mark

Express the following as a rational number:
$\Big(\frac{23}{25}\Big)^\circ$

Answer

$\Big(\frac{23}{25}\Big)^\circ=1$

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Question 881 Mark

Express the following as a rational number:
$\Big(\frac{1}{4}\Big)^{-4}$

Answer

$\Big(\frac{1}{4}\Big)^{-4}=(4)^{4}$
$=4\times4\times4\times4$
$=256$

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Question 891 Mark

Express the following as a rational number:
$5^{-3}$

Answer

$5^{-3}=\Big(\frac{1}{5}\Big)^{3}$
$=\frac{1}{5}\times\frac{1}{5}\times\frac{1}{5}$
$=\frac{1}{125}$

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Question 901 Mark

Express the following in power notation:
$\frac{-27}{64}$

Answer

$\frac{-27}{64}=\frac{(-3)\times(-3)\times(-3)}{4\times 4\times 4}$
$=\Big(\frac{-3}{4}\Big)\times \Big(\frac{-3}{4}\Big)\times \Big(\frac{-3}{4}\Big)$
$=\Big(\frac{-3}{4}\Big)^3$

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Question 911 Mark

Express the following in power notation:
$\frac{25}{36}$

Answer

$\frac{25}{36}=\frac{5\times5}{6\times 6}$
$=\frac{5}{6}\times \frac{5}{6}$
$=\Big(\frac{5}{6}\Big)^2$

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Question 921 Mark

Express the following as a rational number:
$\Big(\frac{-2}{3}\Big)^{-1}$

Answer

$\Big(\frac{-2}{3}\Big)^{-1}=\Big(\frac{3}{-2}\Big)^1$
$=\frac{3}{-2}=\frac{3\times(-1)}{-2\times(-1)}$
$=\frac{-3}{2}$

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Question 931 Mark