Question

Please solve this problem it should be a verified answer please ​

Answer 1

1) Evaluate :

i) 2¹

2¹ = 2

Answer is 2

ii) (4.73)⁰

Anything to the power 0 is 1 so (4.73)⁰ = 1

So the answer is 1

iii) (-1)⁴

When an exponent is in even form then the negative term will become positive

So (-1)⁴ = 1

Answer is 1

$\sf \small v) \: (0.25)^{ - 1}$

Here it is in a-ⁿ form where it is 1/aⁿ

1/(0.25)¹

1/0.25

Answer is 1/0.25

$\sf \small vi) {( \frac{5}{2}) }^{2}$

$\frac{5 \times 5}{2 \times 2}$

$\frac{25}{4}$

Answer is 25/4

$\sf viii) \: ( 1\frac{1}{4} )^{2}$

$\sf {( \frac{5}{4} )}^{2}$

$\sf \frac{5 \times 5}{4 \times 4}$

$\sf \frac{25}{16}$

Answer is 25/16

2)a) Express in exponential form :

I) 10

10¹

ii) 100

10²

iii) 1000

10³

iv) 10000

10⁴

v) 100000

10⁵

b) Express the following products in the smallest exponential form :

I) 16 × 64

So we have to take the bases same and then exponents needs to be added

2⁴ × 2⁶

Applying aⁿ × a¹ we get

${2}^{4 + 6}$

2¹⁰

So the answer is 2¹⁰

ii) 25 × 125

Taking the base as common we get

5² × 5³

5⁵

The answer is 5⁵

iii) 128 ÷ 32

Taking the base 2 as common we get

2⁷ ÷ 2⁵

Now as it is divide we need to substract the exponents

${2}^{7 - 5}$

2²

The answer is 2²

Answer 2

1) Evaluate :

i) 2¹

2¹ = 2

Answer is 2

ii) (4.73)⁰

Anything to the power 0 is 1 so (4.73)⁰ = 1

So the answer is 1

iii) (-1)⁴

When an exponent is in even form then the negative term will become positive

So (-1)⁴ = 1

Answer is 1

(0.25)^-1

Here it is in a-ⁿ form where it is 1/aⁿ

1/(0.25)¹

1/0.25

Answer is 1/0.25