Question

Which shows the following expression using positive exponents?

Answer 1

Answer:

1. option B is correct i.e., $\frac{-3a^{7}b^3b^1}{15a^{2}}$

2. option D is correct i.e., $\frac{a^3b^4}{ab^2}$.

3. option B is correct i.e.,  $\frac{n^{10}}{16m^{6}}$.

Step-by-step explanation:

1. Since the given equation is:

$\frac{-3a^{-2}b^3}{15a^{-7}b^{-1}}$

As we know that $a^{-x}=\frac{1}{a^x}$

So, the given equation can be represented as:

$\frac{-3a^{7}b^3b^1}{15a^{2}}$

2. Given equation is:

$\frac{a^3b^{-2}}{ab^{-4}}$

As we know that $a^{-x}=\frac{1}{a^x}$

so the given equation can be represented as:

$\frac{a^3b^4}{ab^2}$.

3.  Given equation is:

$(\frac{4mn}{m^{-2}n^6})^{-2}$

by using the properties $a^{-x}=\frac{1}{a^x}$,

and $a^x\times a^y=a^{x+y}$

$(\frac{4mn}{m^{-2}n^6})^{-2}$

= $(\frac{4n^1n^{-6}}{m^{-2}m^{-1}})^{-2}$

= $(\frac{4n^{1+(-6)}}{m^{-2+(-1)}})^{-2}$

= $(\frac{4n^{-5}}{m^{-3}})^{-2}$

= $\frac{4^{-2}n^{-5\times (-2)}}{m^{-3\times (-2)}}$

= $\frac{n^{10}}{16m^{6}}$.

which is option B.

Answer 2

1) B. -3a^7b^4/15a^2

2)D. a-^3b^4/ab^2
3) B n^12/16m^2n^2m^4. 2 n's cancel on the top and bottom