**powers**of ten, you should understand the notation and how to work with these powers, as follows:

10 ^{0} = 1

10 ^{1} = 10

10 ^{2} = 10 × 10 = 100

10 ^{3} = 10 × 10 × 10 = 1,000

and so on.

and so on.

To multiply powers of ten, add the exponents.

Multiply the following and leave the answers in powers of ten.

100 × 10

1,000 × 100

0.01 × .001

10,000 × 0.01

0.0001 × 1,000

100 × 10 = 10 ^{2} × 10 ^{1} = 10 ^{(2 + 1)} = 10 ^{3}

1,000 × 100 = 10 ^{3} × 10 ^{2} = 10 ^{(3 + 2)} = 10 ^{5}

0.01 × 0.001 = 10 ^{–2} × 10 ^{–3} = 10 ^{[–2 + (–3)]} = 10 ^{–5}

10,000 × 0.01 = 10 ^{4} × 10 ^{–2} = 10 ^{[4+ (–2)]} = 10 ^{2}

0.0001 × 1,000 = 10 ^{–4} × 10 ^{3} = 10 ^{[–4 + 3]} = 10 ^{–1}

To divide powers of 10, subtract the exponents; that is, subtract the exponent of the second number (the *divisor*) from the exponent of the first number (the dividend).

Divide the following and leave the answers in powers of ten.

1,000 ÷ 100

100 ÷ 10,000

1 ÷ 0.01

0.001 ÷ 0.01

10,000 ÷ 0.1

1,000 ÷ 100 = 10 ^{3} ÷ 10 ^{2} = 10 ^{(3 – 2)} = 10 ^{1}or 10

100 ÷ 10,000 = 10 ^{2} ÷ 10 ^{4} = 10 ^{(2 – 4)} = 10 ^{–2}

1 ÷ 0.01 = 10 ^{0} ÷ 10 ^{–2} = 10 ^{[0 – (–2)]} = 10 ^{(0 + 2)}= 10 ^{2}

0.001 ÷ 0.01 = 10 ^{–3} ÷ 10 ^{–2} = 10 ^{[–3 – (–2)]} = 10 ^{(–3 + 2)}= 10 ^{–1}

10,000 ÷ 0.1 = 10 ^{4} ÷ 10 ^{–1} = 10 ^{[4 – (–1)]} = 10 ^{(4 + 1)}= 10 ^{5}