Powers with positive exponents — lesson. Mathematics State Board, Class 8.

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The number with power

$2$ is called square, and the number with power

$3$ is called cube. We studied this in earlier classes. Do you think the power of number can only be

$2$ and

$3$ ?

No, it's not. The power can be

$4$ ,

$5$ ,

$6$ , …

We read this as

$4$ raised to the power

$2$ .

The exponent of a number shows how many times the number should be multiplied. It is written as a small number to the right and above the base number.

Powers with positive exponents

$2 + 2 + 2 + 2 + 2 + 2 + 2$

$=$

$14$

Here,

$2$ repeatedly added

$7$ times. So, this can be written as

$2 \times 7 = 14$ .

In the same way,

$2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 32$ .

Here,

$2$ repeatedly multiplied

$5$ times. So, this can be written as

$2^5 = 32$

Example:

$2 = 2^1$

$2 \times 2 = 2^2 = 4$

$2 \times 2 \times 2 = 2^3 = 8$

$2 \times 2 \times 2 \times 2 = 2^4 = 16$

$2 \times 2 \times 2 \times 2 \times 2 = 2^5 = 32$

Here, the number

$2$ has powers

$1$ ,

$2$ ,

$3$ ,

$4$ and

$5$ called positive exponents.

Important!

Positive numbers with positive exponents only have positive value.

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1. Powers with positive exponents

Theory: