Question

Find the rational exponent.

• Simplify each expression using the rules of exponents and examine the steps you are taking.

Answer 1

\[(4^{16})^{\frac{ 1 }{ 2 }}\]

Answer 2

\(\normalsize\color{blue}{ (a^b)^c=a^{b \times c} }\)

Answer 3

I think, first off
product rule between exponents

Answer 4

your a=4,
b=16
c=1/2

Answer 5

or i can use the radical property ?

Answer 6

\(\Large (4^{16})^{\frac{ 1 }{ 2 }}\implies 4^{\cancel{ 16 }\cdot \frac{ 1 }{ \cancel{ 2 } }}\)

Answer 7

\[\sqrt{4^{18}}\]

Answer 8

i meant 2 ^18

Answer 9

hmm well.. the 18... ... thought it was 16? =)

Answer 10

\(\bf 16\cdot \frac{ 1 }{ 2 }\implies \frac{ 16 }{ 2 }\)

Answer 11

ohh... yes

Answer 12

is that called radical property ¡

Answer 13

?

Answer 14

hmm I'd think so......

Answer 15

\(\bf \large (4^{16})^{\frac{ 1 }{ 2 }}\implies (2^{2})^{\frac{ 16 }{ 2 }}\implies \sqrt{(2^2)^{16}}\implies \sqrt{(2^{16})^2}\)

Answer 16

Ok i will search out each property in order to write out the paper

Answer 17

http://www.math-worksheet.org/properties-of-exponents

Answer 18

That's very helpful thanks a lot

Answer 19

yw

Answer 20

\[a ^{\frac{ m }{ n }} = \sqrt[n]{a ^{m}}\]

Answer 21

\[\sqrt{4^{16}}\]

Answer 22

\[\sqrt{4^{16}}= 4^{\frac{ 16 }{ 2 }}=4^{8}\]

Answer 23

\[4^{8} = (2*2)^{8}\]

Answer 24

\[(2)^{^{8}}(2)^{8} = 2^{8+8}\]

Answer 25

\[2^{16}\]