What number do you get when you raise any non-zero number to the power of zero ?

Any non-zero number raised to the power of 0 is equal to 1 .

What is a square root of a number?

A square root of a number is a value that, when s quared , gives the original number .

True or False? Every positive number has two square roots .

True. Every positive number has two square roots, one positive and one negative .

True or False? Cube roots of negative numbers do not exist .

False. The cube root of a negative number will also be a negative number. For example, -5 is a cube root of -125.

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What number do you get when you raise any non-zero number to the power of zero?

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What number do you get when you raise any non-zero number to the power of zero?
Any non-zero number raised to the power of 0 is equal to 1.
What is a square root of a number?
A square root of a number is a value that, when squared, gives the original number.
True or False?
Every positive number has two square roots.
True.
Every positive number has two square roots, one positive and one negative.
What function does the symbol $\sqrt{}$ refer to when applied to a positive number?
$\sqrt{}$ refers to the positive square root of a positive number.
For example, $\sqrt{9} = 3$ .
True or False?
Cube roots of negative numbers do not exist.
False.
The cube root of a negative number will also be a negative number.
For example, -5 is a cube root of -125.
Define the term reciprocal.
The reciprocal of a number is the number that you multiply it by to get 1.
For example, $\frac{2}{3}$ is the reciprocal of $\frac{3}{2}$ .
What do you get if you raise a non-zero number to the power of -1?
If you raise a non-zero number to the power of -1 you get the reciprocal of the number.
E.g. $3^{- 1} = \frac{1}{3}$
What do you get if you raise a positive number to the power of ½?
If you raise a non-zero number to the power of ½ you get its positive square root.
E.g. $5^{\frac{1}{2}} = \sqrt{5}$
What is the index law for $a^{m} \times a^{n}$ ?
$a^{m} \times a^{n} = a^{m + n}$ .
If you multiply two powers with the same base number, you add the indices together.
What is the index law for $a^{m} \div a^{n}$ ?
$a^{m} \div a^{n} = a^{m - n}$ .
If you divide two powers with the same base number, you subtract one index from the other.
What is the index law for ${(a^{m})}^{n}$ ?
${(a^{m})}^{n} = a^{m \times n}$ .
If you raise a power to another power, you multiply the indices.
True or False?
$a^{\frac{m}{n}} = (\sqrt[m]{a^{n}})$
False.
$a^{\frac{m}{n}} = {(\sqrt[n]{a})}^{m}$ . The denominator of an index is the root and the numerator of an index is the power.
What does a number written in standard form look like?
A number in standard form looks like $a \times 10^{n}$ . A number between 1 and 10 multiplied by a power of ten.
When a number is written in standard form $a \times 10^{n}$ , which values can $a$ be?
For $a \times 10^{n}$ , $a$ is at least 1 and less than 10, $1 \leq a < 10$ . This means there is one non-zero digit before the decimal point.
When a value between 0 and 1 is written in standard form $a \times 10^{n}$ , what type of number will $n$ be?
If a value is between 0 and 1 then when it is written in standard form, $n$ will be a negative number.
When a number is written in standard form $a \times 10^{n}$ , what type of number can $n$ be?
For $a \times 10^{n}$ , the value $n$ must be an integer. It can be zero, positive or negative.
How do you multiply two numbers that are written in standard form and give the answer in standard form without a calculator?
Multiply together the values of $a$ from both numbers and write this in standard form if needed.
Add together the indices for the powers of 10 from each number.
Multiply the two parts together. Simplify if necessary
How do you divide two numbers that are written in standard form and give the answer in standard form without a calculator?
Divide the values of $a$ for both numbers and write this in standard form if needed.
Subtract the indices for the powers of 10 for both numbers.
Multiply the two parts together. Simplify if necessary
How do you add two numbers that are written in standard form and give the answer in standard form without a calculator?
Rewrite the smaller number so that it has the same power as the larger number.
Add the values of $a$ .
If $a$ is bigger than 10 then divide it by 10 and increase the power of 10 by 1.
How do you subtract two numbers that are written in standard form and give the answer in standard form without a calculator?
Rewrite the smaller number so that it has the same power as the larger number.
Subtract the values of $a$ .
If $a$ is less than 1 then multiply it by 10 and decrease the power of 10 by 1.

1. Numbers & the Number System

2. Equations, Formulae & Identities

3. Sequences, Functions & Graphs

4. Geometry & Trigonometry

5. Vectors & Transformation Geometry

6. Statistics & Probability