# exponentials

• Oct 14th 2010, 11:18 AM
batki610
exponentials
Without a calculator how would I calculate multiplication exponential expression

The formula is a^x a^ y = a ^x+ y

(7 x 10^ 2) x (4 x 10 ^ 5)
i thought the answer would be 28 x 10^ 7 but the answer key has 2.8 x 10 ^ 8
so what am I doing wrong?

in the similar way, (5 x 10 ^ -3) x ( 4 x 10^ -6)
i thought the answer would be 20 x 10 ^ -8 but the answer is 2 x 10 ^-8

Thank you
• Oct 14th 2010, 11:48 AM
e^(i*pi)
Quote:

Originally Posted by batki610
Without a calculator how would I calculate multiplication exponential expression

The formula is a^x a^ y = a ^x+ y

(7 x 10^ 2) x (4 x 10 ^ 5)
i thought the answer would be 28 x 10^ 7 but the answer key has 2.8 x 10 ^ 8
so what am I doing wrong?

in the similar way, (5 x 10 ^ -3) x ( 4 x 10^ -6)
i thought the answer would be 20 x 10 ^ -8 but the answer is 2 x 10 ^-8

Thank you

$\displaystyle 28 = 2.8 \times 10$

They are the same answer but your book is using scientific notation which is of the form $\displaystyle a \times 10^n \text{ where } 1 < a \leq 10 \text{ and } n \in \mathbb{Z}$
(if you don't understand what $\displaystyle \mathbb{Z}$ is - it means the integers)

For your second question it's an arithmetic error on the exponent $\displaystyle -3-6 = -9$ whereas you have -8
• Oct 14th 2010, 11:51 AM
masters
Quote:

Originally Posted by batki610
Without a calculator how would I calculate multiplication exponential expression

The formula is a^x a^ y = a ^x+ y

(7 x 10^ 2) x (4 x 10 ^ 5)
i thought the answer would be 28 x 10^ 7 but the answer key has 2.8 x 10 ^ 8
so what am I doing wrong?

in the similar way, (5 x 10 ^ -3) x ( 4 x 10^ -6)
i thought the answer would be 20 x 10 ^ -8 but the answer is 2 x 10 ^-8

Thank you

Hi batki610,

Your rule is correct: $\displaystyle a^x \cdot a^y=a^{x+y}$

$\displaystyle (5 \times 10^{-3}) \times (4 \times 10^{-6})=$

$\displaystyle (5 \times 4) \times (10^{-3} \times 10^{-6})=$

$\displaystyle 20 \times 10^{-3+(-6)}=$

$\displaystyle 20 \times 10^{-9}=$

$\displaystyle 2.0 \times 10^{-8}$

• Oct 14th 2010, 11:54 AM
Quote:

Originally Posted by batki610
Without a calculator how would I calculate multiplication exponential expression

The formula is a^x a^ y = a ^(x+ y)

(7 x 10^ 2) x (4 x 10 ^ 5)
i thought the answer would be 28 x 10^ 7 but the answer key has 2.8 x 10 ^ 8
so what am I doing wrong?

in the similar way, (5 x 10 ^ -3) x ( 4 x 10^ -6)
i thought the answer would be 20 x 10 ^ -8 but the answer is 2 x 10 ^-8

Thank you

Your answer key is expecting an answer written as a value between 1 and 10 times a power of 10.

$\displaystyle 28=(2.8)(10)=2.8\times 10^1$

Hence

$\displaystyle 28\times 10^7=2.8\times 10^1\times 10^7=2.8\times 10^{1+7}$

You made an error in the second one.

$\displaystyle 10^{-3}\times 10^{-6}=10^{-3-6}$

Finally, express the answer as $\displaystyle 2\times 10^y$