Question

Evaluate each product or quotient. Express the results in scientific notations.

$\left(\mathbf{2}\mathbf{.}\mathbf{5}\times {\mathbf{10}}^3\right)\left(\mathbf{3}\times {\mathbf{10}}^4\right)$

Short answer

The result of$\left(2.5\times {10}^3\right)\left(3\times {10}^4\right)$ is $\mathbf{7}\mathbf{.}\mathbf{5}\times {\mathbf{10}}^7$.

Step-by-step solution

Step 1. Group like terms.

Group like terms in the given expression.

$\left(2.5\times 3\right)\left({10}^3\times {10}^4\right)$

Step 2. Write the property of product of powers.

For any real number a and any integers m and n, $a^m\cdot a^n=a^{m+n}$.

Step 3. Apply property of product of powers.

Apply the property of product of powers to the expression obtained in step 1.

$7.5\times {10}^{3+4}=7.5\times {10}^7$

Therefore, the result of given product is $7.5\times {10}^7$.