Indices and Standard Form

Indices and Standard Form

Let's see how much you've remembered about the last few weeks...

• What is law 1 of the rules of indices?

• Which law are we using when we subtract the powers?

• Can you write a large number in standard form?

• Do you remember how to add together two numbers written in standard form?

During today's lesson...

During this recap lesson some reminders will be shown and then you'll have a chance to complete some questions against your classmates.

Are you ready for your first question?

Fill in the Blanks

Laws of Indices - Law 1

The first law tells us that when multiplying two numbers together that have different powers (eg: 2² x 2³), we can

the powers.

Fill in the Blanks

Laws of Indices - Law 2

The second law tells us that when dividing two numbers together that have different powers (eg: 2³ ÷ 2²), we can

the powers.

Fill in the Blanks

Laws of Indices - Law 3

The third law tells us that when raising one number to the power of another (eg: (2³)² ), we can

the powers.

Laws of Indices

• You need to remember the previous three laws

• Coefficients (numbers in front) are affected by the operation in the question, not the law

• Law 4: Anything to the power of 0 is equal to 1

• Law 5: with negative powers, we can rewrite to 1 over the remaining parts

• Law 6: in fractional powers, the denominator is the root and the numerator is the power underneath the root

Let's try some questions...

Are you ready?

Multiple Choice

Simplify: 3⁵ x 3⁷

• 3¹²
• 9¹²
• 3³⁵
• 9³⁵

Multiple Choice

Simplify: w²⁴ ÷ w⁸

• w¹⁶

• w³

• w³²

• w^24/8

Multiple Choice

Simplify: (y⁷)²

• y¹⁴
• y⁴⁹
• y⁵
• y⁹

Multiple Choice

Simplify: f⁰

• 1
• f
• f¹
• 0

Standard Form

• Used to represent very large or very small numbers

• Positive powers => large numbers

• Negative powers => small numbers

• First number has to be between 1 and 10 (can be 1, can't be 10)

Standard form questions coming next...

Let's check what you remember

Multiple Choice

True or False:

13.7 × 10³ is written in standard form.

• True

• False

Multiple Choice

What is 3 × 10^-2 written

as an ordinary number?

• 300

• 3000

• 0.03

• 0.3

Fill in the Blanks

What is  $4\times10^3$  written as an ordinary number?

Multiple Choice

How do you write 1001 in standard form?

• 1.0001 x 10⁴

• 1.01 x 10⁵

• 1.001 x 10³

• 10.1 x 10³

Let's mix everything up!

Be prepared for questions about everything talked about, all mixed together

Fill in the Blanks

The number 0.000 000 000 067 written in standard form is

 $6.7\ \times10^n$  . What is the value of "n"?

Fill in the Blanks

Express the number below in ordinary form:

 $5.23\times10^4$  

Multiple Choice

The number below, when written is standard form is:

 $21\ 600\ 000$  

•  $216\ \times10^5$  

•  $21.6\ \times10^6$  

•  $2.16\ \times10^7$  

•  $2.16\times10^{-7}$  

Multiple Choice

Why do we need to learn indices and standard form?

• to simplify the actual data

• to expand the actual data

Multiple Choice

a⁷ × a⁴ ÷ a⁵

• a⁷

• a⁶

• a⁴

• a¹¹

Multiple Choice

Which is greater,  2654⁰ or 5⁰?

• 2654⁰
• 5⁰
• They are the same
• Zero is greater

Multiple Choice

(y⁹)^-2

• y¹⁸
• y¹¹
• 1/y¹⁸
• y⁹/2

Multiple Choice

The number below, when written in standard form is:

 $0.000\ 000\ 017\ 3$  

•  $1.73\ \times10^{-8}$  

•  $1.73\ \times10^8$  

•  $17.3\ \times10^{-9}$  

•  $1.73\times10^{-9}$  

Multiple Choice

Simplify the following, giving your answers with positive indices:

 $\left(4a^2b\right)\times\left(6ab^{ }\right)$  

•  $24a^2b^2$  

•  $24a^3b$  

•  $24a^3b^2$  

•  $10a^3b^2$  

Multiple Choice

What is the missing index?

(2⁶)^x = 2¹⁸

• 12

• 3

• 10

• 4

Multiple Choice

Simplify: χ³ ÷ χ²

• χ

• χ⁵

• χ⁶

• χ^-1

• 1/χ

Multiple Choice

Simplify the following:

 $64^{\frac{2}{3}}$  

• 4

• 8

• 16

• 32

Well done!

You have now finished with your Maths for the day!

You can press 'mark as done' on the Google Classroom assignment.