Question

Can anyone help me with “Using the Rules of Exponents? If so, please show me the steps. I have two equations here is the first one division. Thank you.

27 ^-2/3
÷
27 ^-1/3

Answer 1

$$
\cfrac{27^{-\frac{2}{3}}}
{27^{-\frac{1}{3}}}\\
\color{red}{n^{-1}=\cfrac{1}{n}}\\
\cfrac{
\cfrac{1}{27^{\frac{2}{3}}}
}{
\cfrac{1}{27^{\frac{1}{3}}}
}
\implies
\cfrac{27^{\frac{1}{3}}}
{27^{\frac{2}{3}}}\\
\color{red}{27 = 3^3}\\
\cfrac{(3^3)^{\frac{1}{3}}}
{(3^3)^{\frac{2}{3}}}\implies
\cfrac{(3)^{\frac{3}{3}}}
{(3)^{\frac{6}{3}}}\implies \cfrac{3^1}{3^2} \implies \cfrac{1}{3}
$$

Answer 2

Hi Jdoe Thank you for your help. I got as far as 1/27. I am still trying to understand the exponents power rule. Thank you!

Answer 3

yw

Answer 4

Can you show me the steps to this equation?

(a^1/2 b)^1/2 (ab ^1/2)

Answer 5

$$
\cfrac{(a^{\frac{1}{2}}b)^{\frac{1}{2}}}
{2ab^{\frac{1}{2}}} \large ?
$$

Answer 6

Can you show me the steps?

Answer 7

well, first you multiply the exponential to the factors

Answer 8

so \((a^{\frac{1}{2}}b)^{\frac{1}{2}} \) turns into
\((a^{\frac{1}{2}}b)^{\frac{1}{2}} \implies a^{\frac{1}{2}\times \frac{1}{2}} b^{\frac{1}{2}}\)

Answer 9

I worked on this yesterday with someone and was told ^1/2 x ^1/2 = 1^1/4