Question

(x^3) to the 3/4 power. simplify. . Express the product as a radical expression.

Answer 1

\[x^{3^{3/4}}=?\]Is that you want

Answer 2

?

Answer 3

yes

Answer 4

but the x^3 is in parentheses

Answer 5

i believe its \[x^3 \sqrt[4]{x^3}\]

Answer 6

not sure though

Answer 7

ok then using the property\[(a^{n})^{m}=a^{mn}\]
therefore,\[x^{3^{3/4}}= x^{2*3/4}= x^{3/2}=\sqrt[2]{x^{3}}\]

Answer 8

This does not simplify as an expression...

\[\huge (b^m)^n=b^{m\cdot n}\]
\[(b^3)^3=b^3*b^3*b^3=(b*b*b)*(b*b*b)*(b*b*b)=\large b^{3\ \cdot\ 3}=b^9\]

Answer 9

shubham.bagrecha thats not it im afraid.

the answer choices are:

\[x^3[\sqrt[4]{x^3}\]

\[x^2\sqrt[4]{x^3}\]

\[x^2\sqrt[4]{x}\]

\[x\sqrt{x}\]

Answer 10

You can rewrite it but that's technically not "simplified" :-)

Answer 11

I take beef with your question's author :P

Answer 12

okay so how would i rewrite it so it looks like the answer choices i have posted above?

Answer 13

Ah! I see your answer

Answer 14

what is x^(1/2) ;-)

Answer 15

Same as \(\sqrt{x}\), no?

Answer 16

no its just x raised to the power of 1 divided by two

Answer 17

\(\frac{3}{2}\) is the same as 1\(\frac{1}{2}\)

Answer 18

And dividing by a power is the same as taking the n-th root, by definition of what a root is.

Answer 19

okay so whats \[x^3\] raised to the power of 3 divided by 4

Answer 20

. Express the product as a radical expression.

Answer 21

As @shubham.bagrecha said, x\(^{3/2}\)

Write it out expanded like did initially! It'll help ;-)

Answer 22

Does writing it like this help?
\[\sqrt{x*x*x}\]

Answer 23

What is \(\sqrt{x*x}\) = ? ;-)

Answer 24

x right?

Answer 25

Or with 2's \(\sqrt{2*2*2}\)

Answer 26

we can write it as \[x^{2/2}*x^{1/2}=x^{3/2}\]
=\[=x*\sqrt{x}=x^{3/2}\]

Answer 27

Yep that's right

Answer 28

So the fourth option is the asn.

Answer 29

yes

Answer 30

Again, it's not technically "simplified" just rewritten. Simplification just means having everything in base form, in layman's terms. But good enough. This is trying to see if you understand the concept of what to do with fractional exponents. Rules of exponents.