03. Indices

Indices

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Question 1: 

Simplify the following expressions:

 

1(a) x^2 \times x^8

 

ANSWER: Multiple choice (Type 1)

A: x^{10}

B:  x^{16} 

C:  x^{14}

D:  x^6

 

Workings: x^2 \times x^8 = x^{2+8}

Marks = 1

 

1(b) a^2 \div a^8

 

ANSWER: Multiple choice (Type 1)

A: a^{-10}

B:  a^{-16 }

C:  a^{-4}

D:  a^{-6}

 

Workings: a^2 \div a^8 = a^{2-8}=a^{-6}

Marks = 1

 

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Question 2: 

Simplify the following expressions:

 

2(a) (4x)^{-2}

 

ANSWER: Multiple choice (Type 1)

A: \dfrac{1}{8x^2}

B: \dfrac{1}{16x^2}

C: \dfrac{1}{4x^2}

D:  \dfrac{4}{x^2}

 

Workings:  (4x)^{-2} = \dfrac{1}{(4x)^2} =\dfrac{1}{16x^2}

Marks = 1

 

2(b) (8)^{\frac{2}{3}}

 

ANSWER: Multiple choice (Type 1)

A: 2

B: 4

C: 6

D:  3

 

Workings:  (8)^{\frac{2}{3}} = (\sqrt[3]{8})^2 = 2^2 = 4

Marks = 1

 

2(c) (4)^{-\frac{3}{2}}

 

ANSWER: Multiple choice (Type 1)

A: \dfrac{1}{2}

B: \dfrac{1}{4}

C: \dfrac{1}{6}

D:  \dfrac{1}{8}

 

Workings:  (4)^{-\frac{3}{2}} = \dfrac{1}{4^{3/2}} = \dfrac{1}{\sqrt{4}^3}=\dfrac{1}{8}

Marks = 1

 

2(d) \sqrt{81^{\frac{1}{2}}\times 2^4}

 

ANSWER: Multiple choice (Type 1)

A: 6

B: 8 

C: 10 

D:  12

 

Workings:  \sqrt{81^{\frac{1}{2}}\times 2^4} = \sqrt{9\times 16} = \sqrt{144} = 12

Marks = 2

 

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Question 3: 

Simplify the following expression:

 

\dfrac{5^2 \times 5 ^{-4}}{5^3}

 

ANSWER: Multiple choice (Type 1)

A: \dfrac{1}{25}

B: \dfrac{1}{125}  

C: \dfrac{1}{625}  

D:  \dfrac{1}{3125}

 

Workings:  \dfrac{5^2 \times 5 ^{-4}}{5^3} =  \dfrac{5^{-2}}{5^3} = 5^{-2-3}= 5^{-5}= \dfrac{1}{25}

Marks = 2

 

 

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Question 4: 

Simplify the following expression:

 

\dfrac{5x^2y^3 \times 2x^4y^{-2}}{10x^6y}

 

ANSWER: Multiple choice (Type 1)

A: \dfrac{1}{y}

B: \dfrac{1}{y^2}  

C: \dfrac{100x}{y}  

D:  \dfrac{10x}{y^2}

 

Workings:  \dfrac{5x^2y^3 \times 2x^4y^{-2}}{10x^6y}= \dfrac{1x^6y^{-1}}{10x^6y}=\dfrac{y^{-1}}{y} = y^{-2} = \dfrac{1}{y^2}

Marks = 2

 

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Question 5: 

Write the following expression as a power of 5:

 

\dfrac{25^5}}{5^3}

 

ANSWER: Multiple choice (Type 1)

A: \dfrac{1}{y}

B: \dfrac{1}{y^2}  

C: \dfrac{100x}{y}  

D:  \dfrac{10x}{y^2}

 

Workings:  \dfrac{25^5}}{5^3} = \dfrac{5^6}}{5^3} = 5^{6-3} = 5^3

Marks = 2

 

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Question 6: 

Calculate the following:

 

6(a) 27^\frac{2}{3}

 

ANSWER: Multiple choice (Type 1)

A: 1

B: 3  

C: 9

D:  27

 

Workings:  27^\frac{2}{3} = (\sqrt[3]{27})^2=3^2 = 9

Marks = 1

 

 

6(b) 32^\frac{3}{5}

 

ANSWER: Multiple choice (Type 1)

A: 2

B: 4 

C: 6

D:  8

 

Workings:  32^\frac{3}{5} = (\sqrt[5]{32})^3 = 2^3 = 8 

Marks = 1

 

 

6(c) 64^\frac{3}{2}

 

ANSWER: Multiple choice (Type 1)

A: 4096

B: 1024 

C: 512

D:  64

 

Workings:  64^\frac{3}{2} = (\sqrt[2]{64})^3 = 8^3 = 512 

Marks = 1

 

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Question 7: 

 

7(a) Express \sqrt[3]{y} in the form y^k

 

ANSWER: Multiple choice (Type 1)

A: y^3

B: y^{3k} 

C: y^{\frac{3}{k}}

D:  y^{\frac{1}{3}}

 

Workings:  \sqrt[3]{y}=y^{\frac{1}{3}}

Marks = 1

 

 

7(b) Express \dfrac{1}{y\sqrt{y}} in the form y^k

 

ANSWER: Multiple choice (Type 1)

A: y^3

B: y^{3k} 

C: y^{\frac{3}{k}}

D:  y^{\frac{1}{3}}

 

Workings:  \dfrac{1}{y\sqrt{y}=\dfrac{1}{\sqrt{y^3}}=y^{-3/2}

Marks = 3

 

 

7(c) Express \sqrt{2 \frac{1}{4}} as a decimal.

 

ANSWER: Multiple choice (Type 1)

A: 1.5 

B: 2.5

C: 0.5

D:  3.5

 

Workings: \sqrt{2 \frac{1}{4}} = \sqrt{\dfrac{9}{4}}=\dfrac{\sqrt{9}}{\sqrt{4}}= \dfrac{3}{2} = 1.5

Marks = 2