Question

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

$\frac{\mathbf{8}\mathbf{.}\mathbf{8}\times {\mathbf{10}}^2}{\mathbf{4}\times {\mathbf{10}}^{-\mathbf{4}}}$

Short answer

The value of$\frac{8.8\times {10}^2}{4\times {10}^{-4}}$ is $\mathbf{2}\mathbf{.}\mathbf{2}\times {\mathbf{10}}^6$.

Step-by-step solution

Step 1. Group powers with same base.

Group powers with same base in the given quotient.

$\left(\frac{8.8}{4}\right)\left(\frac{{10}^2}{{10}^{-4}}\right)$

Step 2. Write the rule of quotient of powers.

For any nonzero number x, and any integers m and n, $\frac{x^m}{x^n}=x^{m-n}$.

Step 3. Apply the rule of quotient of powers and simplify.

Apply the rule of quotient of powers to step 1 and simplify further.

$\left(\frac{8.8}{4}\right){10}^{2-\left(-4\right)}=2.2\times {10}^6$

Therefore, value of a given quotient is $2.2\times {10}^6$.