Question

Pls read to picture below

Answer 1

1) 6a

2) 8

3) 18a

Explanation:

1)
`\sf {2a}^( - 1) * {3a}^(2)`

Simplify using exponent rule with the same base

`\sf \: 2 * {3a}^( - 1 + 2)`

Multiply the monomials

`\sf \: 6a {}^( - 1 + 2)`

Calculate the sum or difference.

`\sf \: {6a}^(1)`

Calculate the power

`\sf \: 6a`

2)
`\sf( (1)/(2) ) {}^( - 3)`

simplify using negative exponents rule
`\sf {a}^(-n) = \frac{1}{{a}^(n)}`

`\sf {2}^(3)`

calculate the power

`\sf \: 8`

3)
`\sf {2a}^( - 1) * {(3a)}^(2)`

Simplify using exponents rule with the same exponent

`\sf {2a}^(-1) × {3}^(2) × {a}^(2)`

Simplify using exponents rule with the same base a ^ n + a ^m = a ^n+m

`\sf 2×{3}^(2) ×{a}^(-1+2)`

Calculate the power

`\sf 2 × 9a {}^(-1+2)`

`\sf 18a`

2(I) We round a number to three significant figures in the same way that we would round to three decimal places. We count from the first non-zero digit for three digits. We then round the last digit. We fill in any remaining places to the right of the decimal point with zeros.

8348 = 8350(rounded to 3 SF)

2(ii) 0.00796 = 0.0080

2(II) 6.329 = 6

2(III) 0.05684 = 0.0568

Answer 2

Explanation:

1.i

2a^-1 × 3a²

remember, when we multiply factors with the same base value or variable, we keep that base value or variable and simply add the exponents.

-1 + 2 = 1

so, we get

2×3 × a¹ = 6a

1.ii

(1/2)^-3

remember, the "-" on the exponent just means 1/...

so, it is actually

1 / (1/2)³ = 1 / 1/8 = 8

1.iii

2a^-1 × (3a)²

similar to the first one, but remember, when we put the product of factors to a certain power, we need to do this for every factor of the inner multiplication :

2a^-1 × 9a² = 2×9 × a¹ = 18a

2.

the first significant figure is the first digit in the number reading from the left, that is not 0. it can be before or after the decimal point.

any digit (now continuing to read further to the right) after the first significant figure is again a significant figure even if it is 0.

i.

8.348 is rounded to 3 significant figures : 8.35

ii.

0.00796 is rounded to 2 significant figures :

0.0080 or 0.008 (because if the last digit after the decimal point is a 0, we can ignore it).

iii.

6.329 is rounded to 1 decimal place : 6.3

iv.

0.05684 is rounded to 3 decimal places : 0.057

3.

the sum of interior angles in a polygon is (n − 2) × 180°. where n is the number of sides.

as deca stands for 10, a decagon has 10 sides and 10 vertexes.

the sum of its inner angles is

(10 - 2) × 180° = 8 × 180° = 1440°

1170° of that is already covered by the first 7 angles.

so, we have left

1440 - 1170 = 270°

for the remaining 3 angles (that are all equal).

so,

270 = 3×angle

angle = 270/3 = 90°.

so, all of the 3 remaining angles are 90°.