Powers with Negative Exponents

Answer the below Quiz questions.

As the exponent decreases by 1, the value becomes of the previous value.

With the above knowledge let's find the value of 10^1

10−1 = Previous value10 = 10010 = 110

10−2 = Previous value10 = = 110÷10 = 110x110 = 1100 =

10−3 = Previous value100 = = 1100÷10 = 1100x110 = 11000 =

Let's see if the same thing works for base 3 instead of 10.

Let us see for the negative powers.

we say, 3−1 = 1 ÷ 3 =

And 3−2 =13 ÷ 3 = 13x3

3−3 = 132 ÷ 3 = 132 x 13=

In general, we can say that for any non-zero integer a, a−m = 1am, where m is a positive integer. a−m is the multiplicative inverse of am.

Try these.

Match the below exponents

2^(–2)

10^(–5)

7^(–2)

5^(–3)

10^(-100)

1/5^3

1/2^2

1/10^100

1/7^2

1/10^5

Expand the following numbers using exponents.

We learnt how to write numbers like 1425 in expanded form using exponents as

1425 = 1 x 1000 + 4 x 100 + 2 x 10 + 5 x 1

1425 = 1 × + 4 × + 2 × + 5 × .

Let us see how to express 1425.36 in expanded form in a similar way.

1425.36 = 1 × 1000 + 4 × 100 + 2 × 10 + 5 × 1 + 310 + 6100

1 × + 4 × + 2 × + 5 × + 3 × + 6 ×

Expand the following numbers using exponents.

We learnt how to write numbers like 1025.63 in expanded form using exponents as

(i) 1025.63 = 1 × + 2 × + 5 × + 6 × + 2 ×

(ii) 1256.249 = 1 × + 2 × + 5 × + 6 × + 2 × + 4 × + 9 ×