Albert Teen YOU ARE LEARNING:  Indices: Higher Powers  # Indices: Higher Powers ### Indices: Higher Powers

Higher powers make numbers bigger very very quickly!

The index number $5^2$ is the same as_____ The index number $7^3$ is the same as______ Using the same principle as square and cube numbers, what is $2^5$ the same as? What is $4^6$ the same as in the form $x \times x \times x...$? 1

Index numbers like $5^7$ are made up of a base number and a power. Which number is the power? 2

In the index number $5^7$:

The base number is $5$ The power is $7$

3

What is the base in the expression $a^n$? 4

Sometimes the power is also called the index.

In $a^n$ we can say $n$ is the power or the index.

1

Increasing powers makes numbers higher very very quickly!

For example, $5^1$ is just $5$, while $5^5$ is $3,125$ 2

When numbers get very big very quickly like this

it is known as exponential growth. What does $3^4$ actually equal? What does $2^5$ equal? 1

A useful power to know is the power $1$. What do you think $2^1$ equals? 2

Now find $12^1$. 3

From this we can see that any number raised to the power $1$ is itself.

$x^1=x$

Summary!

1

Powers tell you how many times you should multiply the number by itself

For example $4^6$ is the same as $4$ multiplied by itself 6 times.

$4 \times 4 \times 4 \times 4 \times 4 \times 4$

2

Any number raised to the power $1$ is itself.

$x^1=x$

3

In the expression $x^y$

$x$ is the base number $y$ is the power

4

Increasing powers makes numbers higher very very quickly!

For example, $3^1$ is just $3$, while $3^8$ is $6,561$