# How do you evaluate (7.5times10^6)(2.6times10^-2)?

May 31, 2017

The answer is $19.5 \times {10}^{4}$, or $1.95 \times {10}^{5}$.

#### Explanation:

Evaluate:

$\left(7.5 \times {10}^{6}\right) \left(2.6 \times {10}^{- 2}\right)$

If you are not using a calculator, multiply the two coefficients, $7.5$ and $2.6$.

$7.5 \times 2.6 = 19.5$

Next multiply the powers of the base $10$.

${10}^{6} \times {10}^{- 2}$

Use the product rule of exponents: ${a}^{m} {a}^{n} = {a}^{m + n}$

${10}^{6 + \left(- 2\right)} = {10}^{4}$

Put everything back together.

$19.5 \times {10}^{4}$

If you want the answer in scientific notation, move the decimal one place to the left and increase the exponent to by $1$.

$1.95 \times {10}^{5}$