Question

First rewrite into exponential form. Then use properties of exponents to simplify each expression. Leave your answer in exponential form.

Answer 1

Step-by-step explanation:

Question 2

To answer the question, we will use the exponential laws

`\begin{gathered} a^{(1)/(b)}=\sqrt[b]{a} \\ a^(-1)=(1)/(a) \\ a^{(b)/(c)}=\sqrt[c]{a^b} \\ a^b* a^c=a^(b+c) \\ a^b/ a^c=a^(b-c) \end{gathered}`

Applying these laws

Question 2a

`\sqrt[4]{(mn)^(12)}=(mn)^{(12)/(4)}`
`\sqrt[4]{(mn)^(12)}=(mn)^{(12)/(4)}=(mn)^3`

Question 2b

`√(x).\sqrt[7]{x}`

we will rewrite it as

`x^{(1)/(2)}* x^{(1)/(7)}=x^{(1)/(2)+(1)/(7)}=x^{(9)/(14)}`

Question 2c

`\frac{\sqrt[6]{x}}{\sqrt[4]{x}}=\frac{x^{(1)/(6)}}{x^{(1)/(4)}}`

Then

`\frac{x^{(1)/(6)}}{x^{(1)/(4)}}=x^{(1)/(6)-(1)/(4)}=x^{-(1)/(12)}=(1)/(x^(12))`

Question 2d

`\sqrt[6]{(r^6)/(s^(18))}=((r^6)/(s^(18)))^{(1)/(6)}`

Simplifying further

`\frac{r^{(6)/(6)}}{s^{(18)/(6)}}=(r)/(s^3)`

Question 2e

`\sqrt[3]{x^6q^9}=(x^6q^9)^{(1)/(3)}`

Simplifying further

`(x^6q^9)^{(1)/(3)}=x^{(6)/(3)}q^{(9)/(3)}=x^2q^3`

Question 2f

`√(49x^5)=(49x^5)^{(1)/(2)}`

Simplifying further

`49^{(1)/(2)}x^{(5)/(2)}=7x^{(5)/(2)}`