Question

8 \cdot 10^48⋅10 4 8, dot, 10, start superscript, 4, end superscript is how many times as large as 4\cdot10^{-5}4⋅10 −5 4, dot, 10, start superscript, minus, 5, end superscript?

Answer 1

Answer:

$\bold{2\cdot10^9}$

Step-by-step explanation:

The given expression s are:

$8 \cdot 10^4$ and

$4\cdot10^{-5}$

To find:

$8 \cdot 10^4$ is how many times  as large as $4\cdot10^{-5}$.

Solution:

Let $8 \cdot 10^4$ is $x$ times as large as $4\cdot10^{-5}$.

So, we can say that:

$8 \cdot 10^4$  = $4\cdot10^{-5}$$\times$ $x$

OR

$x= \dfrac{8\cdot 10^4}{4\cdot 10^{-5}}$

Let us have a look at the formula for exponents:

$\dfrac{x^p}{x^q} = x^{p-q}$

Here we have:

$x=10\\p=4\ and\\q=-5$

Solving the expression using above formula:

$\Rightarrow x= \dfrac{8}{4}\cdot 10^{4-(-5)}} = \bold{2\cdot10^9}$

So, Let $8 \cdot 10^4$ is $\bold{2\cdot10^9}$ times as large as $4\cdot10^{-5}$