MCQ

MCQ 11 Mark

$\bigg\{\Big(\frac{1}{3}\Big)^2\bigg\}^4$ is equal to:

A
$\Big(\frac{1}{3}\Big)^6$
✓
$\Big(\frac{1}{3}\Big )^8$
C
$\Big(\frac{1}{3}\Big)^{24}$
D
$\Big(\frac{1}{3}\Big)^{16}$

Answer

Correct option: B.

$\Big(\frac{1}{3}\Big )^8$

We have:
$\bigg(\Big(\frac{1}{3}\Big)^2\bigg)^4$
$=\Big (\frac{1}{3}\Big)^{2\times4}$
$=\Big(\frac{1}{3}\Big)^8$

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MCQ 21 Mark

For any two non$-$zero rational nmbers $a,(\text{a}^3)^{-2}$ is equal to:

A
$\text{a}^9$
✓
$\text{a}^{-6}$
C
$\text{a}^{-9}$
D
$\text{a}^1$

Answer

Correct option: B.

$\text{a}^{-6}$

$(\text{a})^{-2}=\text{a}^3\times(-2)$
$=\text{a}^{-6}$

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MCQ 31 Mark

$\Big(\frac{2}{3}\Big)^{-5}\times\Big(\frac{5}{7}\Big)^{-5}$ is equal to:

A
$\Big(\frac{2}{3}\times\frac{5}{7}\Big)^{-10}$
✓
$\Big(\frac{2}{3}\times\frac{5}{7}\Big )^{-5}$
C
$\Big(\frac{2}{3}\times\frac{5}{7}\Big)^{25}$
D
$\Big(\frac{2}{3}\times\frac{5}{7}\Big)^{-25}$

Answer

Correct option: B.

$\Big(\frac{2}{3}\times\frac{5}{7}\Big )^{-5}$

We have:
$\Big(\frac{2}{3}\Big)^{-5}\times\Big(\frac{5}{7}\Big)^{-5}$
$=\Big(\frac{2}{3}\times\frac{5}{7}\Big)^{-5}$

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MCQ 41 Mark

Which of the following number is not equal to $\frac{-8}{27}?$

✓
$\Big(\frac{2}{3}\Big)^{-3}$
B
$-\Big(\frac{2}{3}\Big)^3$
C
$\Big(-\frac{2}{3}\Big)^3$
D
$\Big(\frac{-2}{3}\Big)\times\Big(\frac{-2}{3}\Big )\times\Big(\frac{-2}{3}\Big)$

Answer

Correct option: A.

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

We can write $\frac{-8}{27}$ as $\frac{-2\times(-2)\times(-2)}{3\times3\times3}$ it can be written in the foms given below.
$\frac{-2\times(-2)\times(-2)}{3\times3\times3}=\frac{2\times2\times2}{3\times3\times3 }$
$=-\frac{2}{3}\times\frac{2}{3}\times\frac{2}{3}$
$=-\Big(\frac{2}{3}\Big)^3$

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MCQ 51 Mark

$\Big(\frac{-1}{2}\Big)^5\times\Big(\frac{-1}{2}\Big)^3$ is equal to:

✓
$\Big(\frac{-1}{2}\Big)^{8}$
B
$-\Big(\frac{1}{2}\Big)^8$
C
$\Big(\frac{1}{4}\Big)^8$
D
$\Big(-\frac{1}{2}\Big)^{15}$

Answer

Correct option: A.

$\Big(\frac{-1}{2}\Big)^{8}$

We have:
$\Big(\frac{-1}{2}\Big)^5\times\Big(\frac{-1}{2}\Big)^3$
$=\Big(\frac{-1}{2}\Big)^{5+3}$
$=\Big(\frac{-1}{2}\Big)^8$

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MCQ 61 Mark

For any two non$-$zero rational nmbers $a$ and $b,\text{a}^{4}\div\text{b}^4$ is equal to:

A
$(\text{a}\div\text{b})^1$
B
$(\text{a}\div \text{b})^0$
✓
$(\text{a}\div \text{b})^4$
D
$(\text{a}\div \text{b})^8$

Answer

Correct option: C.

$(\text{a}\div \text{b})^4$

This is one of the basic exponential formulae, i.e. $(\text{a}\div\text{b})^\text{n}=\text{a}^\text{n}\div\text{b}^\text{n}$

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MCQ 71 Mark

$\Big(\frac{1}{5}\Big)^0$ is equal to:

A
$0$
✓
$\frac{1}{5}$
C
$1$
D
$5$

Answer

Correct option: B.

$\frac{1}{5}$

We have:
$\Big(\frac{1}{5}\Big)^0=1$

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MCQ 81 Mark

For any two non$-$zero rational nmbers $a, \text{a}^7\div\text{a}^{12}$ is equal to:

A
$\text{a}^5$
B
$\text{a}^{-19}$
✓
$\text{a}^{-5}$
D
$\text{a}^{19}$

Answer

Correct option: C.

$\text{a}^{-5}$

$\text{a}^\text{m}\div\text{a}^\text{n}=\text{a}^{\text{m}-\text{n}}$
Hence,
$\text{a}^\text{7}\div\text{b}^{12}=\text{a}^{7-12}=\text{a}^{-5}$

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MCQ 91 Mark

Square of $\Big(\frac{-2}{3}\Big)$ is:

A
$-\frac{2}{3}$
B
$\frac{2}{3}$
C
$-\frac{4}{9}$
✓
$\frac{4}{9}$

Answer

Correct option: D.

$\frac{4}{9}$

To square a number is to raise it to the power of $2.$
Hence, thesquare of $\Big(\frac{-2}{3}\Big)$ is $\frac{(-2)^2}{3^2}=\frac{4}{9}$

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MCQ 101 Mark

$\Big(\frac{2}{3}\Big)^{-5}$ is equal to:

A
$\Big(\frac{-2}{3}\Big)^5$
✓
$\Big(\frac{3}{2}\Big)^5$
C
$\frac{2\text{x}-5}{3}$
D
$\frac{2}{3\times5}$

Answer

Correct option: B.

$\Big(\frac{3}{2}\Big)^5$

Rearrange $\Big(\frac{2}{3}\Big)^{-5}$ to get a positive exponent.
$\Big(\frac{2}{3}\Big) ^{-5}=\frac{1}{\big(\frac{2}{3}\big)^5}$
$=\frac{1}{2^5}$
$=\frac{\frac{3^5}{2^5}}{3^5}$
$=\frac{3^5}{2^5}$
$=\Big (\frac{3}{2}\Big)^5$

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MCQ 111 Mark

Which of the following is not equal to $\Big(\frac{-3}{5}\Big)^4?$

A
$\frac{(-3)^4}{5^4}$
B
$\frac{3^4}{(-5)^4}$
✓
$-\frac{3^4}{5^4}$
D
$\frac{-3}{5}\times\frac{-3}{5}\times\frac{-3}{5}\times\frac{-3}{5}$

Answer

Correct option: C.

$-\frac{3^4}{5^4}$

$\Big(\frac{-3}{5}\Big)^4=\frac{(-3)^4}{5^4}=\frac{3 ^4}{(-5)^4}=\frac{-3}{5}\times\frac{-3}{5}\times\frac{-3}{5}\times\frac{-3}{5}$
It is not equal to $-\frac{3^4}{5^4}.$

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MCQ 121 Mark

$\Big(\frac{-3}{2}\Big)^{-1}$ is equal to:

A
$\frac{2}{3}$
✓
$-\frac{2}{3}$
C
$\frac{3}{2}$
D
none of these.

Answer

Correct option: B.

$-\frac{2}{3}$

We have:
$\Big(\frac{-3}{2}\Big)^{-1}$
$=\frac{1}{\frac{(-3)}{2}}$
$=\frac{2}{-3}$

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MCQ 131 Mark

Which of the following is not equal to $\Big(\frac{2}{3}\Big)^4?$

A
$\Big(\frac{3}{2}\Big)^4$
B
$\Big(\frac{2}{3}\Big)^{-4}$
✓
$\Big(\frac{3}{2}\Big)^{-4}$
D
$\frac{3^4}{2^4}$

Answer

Correct option: C.

$\Big(\frac{3}{2}\Big)^{-4}$

The reciprocal of $\Big(\frac{2}{3}\Big)^{4}$ is $\Big(\frac{3}{2}\Big)^{4}$
Therefore, option $(a)$ is the correct answer.
Option $(b)$ is just re$-$expressing the number with a negative exponent.
Option $(d)$ is obtained by working out the exponent.
Hence,option $(c)$ is not the reciprocal of $\Big(\frac{2}{3}\Big )^4$

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MCQ 141 Mark

$\Big(\frac{-1}{3}\Big)^3\div\Big(\frac{-1}{5}\Big)^8$ is equal to:

A
$\Big(\frac{-1}{5}\Big)^{5}$
B
$\Big(-\frac{1}{5}\Big)^{11}$
✓
$(-5)^5 $
D
$\Big(\frac{1}{5}\Big)^{5}$

Answer

Correct option: C.

$(-5)^5 $

We have:
$\Big(\frac{-1}{5}\Big)^3\div\Big(\frac{-1}{5}\Big)^8$
$=\Big(\frac{-1}{5}\Big)^{3-8}$
$=\Big(\frac{-1}{5}\Big)^{-5}$
$=\frac{1}{\big(\frac{-1}{5}\big)^5}$
$=\frac{1}{\big(\frac{(-1)^5}{5^5}\big)}$
$=\frac{5^5}{(-1)^5}$
$=\Big(\frac{5}{-1}\Big )^5$
$=(-5)^5$

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MCQ 151 Mark

$\Big(\frac{-2}{5}\Big)^7\div\Big(\frac{-2}{5}\Big)^5$ is equal to:

A
$\frac{4}{25}$
B
$\frac{-4}{25}$
✓
$\Big(\frac{-2}{5}\Big)^{12}$
D
$\frac{25}{4}$

Answer

Correct option: C.

$\Big(\frac{-2}{5}\Big)^{12}$

We have:
$\Big(\frac{-2}{5}\Big)^7\div\Big(\frac{-2}{5}\Big)^5$
$=\Big(\frac{-2}{5}\Big)^{7-5}$
$=\Big(\frac{-2}{5}\Big)^{2}$
$=\frac{(-2)^2}{5^2}$
$=\frac{4}{25}$

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MCQ 161 Mark

Cube of $\frac{-1}{2}$ is:

A
$-\frac{1}{3}$
B
$\frac{1}{16}$
✓
$-\frac{1}{8}$
D
$\frac{-1}{16}$

Answer

Correct option: C.

$-\frac{1}{8}$

The cube of a number is the number raised to the power of $3.$
Hence the cube of $-\frac{1}{2}$ is $\frac{(-1)^3}{2^3}$
$=-\frac{1}{8}$

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MCQ 171 Mark

For any two non$-$zero rational nmbers $a $ and $b,\text{a}^{4}\div\text{b}^4$ is equal to:

A
$(\text{a}\times\text{b})^0$
B
$(\text{a}\times\text{b})^{10}$
✓
$(\text{a}\times\text{b})^5$
D
$(\text{a}\times\text{b})^{25}$

Answer

Correct option: C.

$(\text{a}\times\text{b})^5$

$\text{a}^{\text{n}}\times\text{b} ^{\text{n}}=(\text{a}\times{\text{b}} )^\text{n}$
Hence,
$\text{a}^\text{5}\times\text{b}^5=(\text{a}\times\text{b} )^5$

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MCQ 181 Mark

$\Big(\frac{3}{4}\Big)^{5}\div\Big(\frac{5}{3}\Big)^{5}$ is equal to:

✓
$\Big(\frac{3}{4}\div\frac{5}{3}\Big)^5$
B
$\Big(\frac{3}{4}\div\frac{5}{3}\Big)^1$
C
$\Big(\frac{3}{4}\div\frac{5}{3}\Big)^0 $
D
$\Big(\frac{3}{4}\div\frac{5}{3}\Big)^{10} $

Answer

Correct option: A.

$\Big(\frac{3}{4}\div\frac{5}{3}\Big)^5$

We have:
$\Big(\frac{3}{4}\Big)^{5}\div\Big(\frac{5}{3}\Big)^{5}$
$=\Big( \frac{3}{4}\div\frac{5}{3}\Big)^5$

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