## Podcast Beta

## Questions and Answers

The value of if a = 4, b = âˆ’2 and c = âˆ’3 is:

Simplifying the expression gives:

When the brackets are expanded, the expression becomes:

The first index law states that is equal to:

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Which of the following expressions is the same as (5*m*)^2?

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3.20405 written to 4 significant figures is?

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Simplify the following.

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Expand and simplify the following.

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Factorise the following.

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Express the following with positive indices.

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Simplify the following using the index laws.

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## Study Notes

### Algebra and Indices

#### Simplifying Expressions

- Simplifying the expression
`a^2 + 2a - 3`

gives`a^2 + 2a - 3`

- Simplifying the expression
`2a^2 + 3a - 1`

gives`2a^2 + 3a - 1`

#### Index Laws

- The first index law states that
`a^m Ã— a^n = a^(m+n)`

- The second index law states that
`a^m Ã· a^n = a^(m-n)`

- The third index law states that
`(a^m)^n = a^(mÃ—n)`

#### Expanding and Simplifying

- Expanding and simplifying the expression
`(a + b)^2`

gives`a^2 + 2ab + b^2`

- Expanding and simplifying the expression
`(a - b)^2`

gives`a^2 - 2ab + b^2`

#### Factorising

- Factorising the expression
`a^2 + 2a - 3`

gives`(a + 1)(a - 3)`

- Factorising the expression
`2a^2 + 3a - 1`

gives`(2a - 1)(a + 1)`

#### Index Laws Applications

- Expressing the expression
`5x^3y / 10x^5y^3`

with positive indices gives`1/2x^2y^2`

- Expressing the expression
`6p^6(s^2)^0 / 2(p^4s^2)^2`

with positive indices gives`3/p^2s^4`

#### Scientific Notation

- Writing the number 150 000 000 in scientific notation gives
`1.5 Ã— 10^8`

- Writing the number 0.0000075 in scientific notation gives
`7.5 Ã— 10^-6`

#### Distance and Speed

- The largest distance between Earth and Mars is approximately 400 000 000 km
- The speed of light is approximately 300 000 km/s

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## Description

Test your understanding of algebra and indices with this 5-question multiple-choice quiz, covering topics such as expression simplification and index laws.