Question

What is the simplified form of ? Please help me :) Medal and Fan :)

Answer 1

looks "very" simplified already
since it looks blank, it has to be simplified

Answer 2

\[\sqrt[3]{-49x}\times \sqrt[3]{7x ^{2}}\]

Answer 3

Seems to me like you need to use the law of exponents, recall that:

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

And

\[x^n \times x^m=x^{m+n}\]

Does this help, or do you need more help?

Answer 4

\(\large {
\sqrt[3]{-49x}\times \sqrt[3]{7x ^{2}}\qquad {\color{brown}{ 7^2=49 }}\qquad thus
\\ \quad \\
\sqrt[3]{-7^2x}\times \sqrt[3]{7x ^{2}}\implies \sqrt[3]{-7^2x\cdot 7x^2}
\\ \quad \\
\sqrt[3]{-7^2\cdot 7^1\cdot x^1\cdot x^2}\implies

\sqrt[3]{-7^{2+1}\cdot x^{1+2}}\implies ?
}\)

Answer 5

I need more help. My teacher never taught me this.

Answer 6

Um give me a moment to read :)

Answer 7

\[\sqrt[3]{-7^{3}}timesx ^{3}\]

Answer 8

Im uncertain about what i have to do next

Answer 9

well... hmm yes sorta \(\Large \sqrt[3]{-7^{2+1}\cdot x^{1+2}}\implies \sqrt[{\color{blue}{ 3}}]{-7^{\color{blue}{ 3}}x^{\color{blue}{ 3}}}\)

so... can we take anything from the radical?

Answer 10

bear in mind that \(\bf -7\cdot -7\cdot -7\implies -7^3
\\ \quad \\
+x\cdot +x\cdot +x\implies +x^3\)

Answer 11

the exponent in the radicand, matches the root
thus if that's the case, then the "radicand jumps off the fence" of the radical to outside

Answer 12

a negative number, and an even root, like say square root
wouldn't work

but that's not true for "even" roots like 3, or 5, or 7
they can have negative radicands and yield a value

Answer 13

\(\large \bf \sqrt[3]{-7^{2+1}\cdot x^{1+2}}\implies \sqrt[{\color{blue}{ 3}}]{-7^{\color{blue}{ 3}}x^{\color{blue}{ 3}}}\implies -7x\sqrt[3]{\qquad }
\\ \quad \\
-7x\)

Answer 14

I really dont understand what i have to do next my teacher has a tough accent and is not perfect..........thats the answer?

Answer 15

well... notice the -7 at the 3rd degree, the x at the 3rd degree
and the root at the 3rd level as well
match

so the -7 comes out, the x comes out
leaving nothing inside

Answer 16

they come out, without their exponent of course

Answer 17

thats what you showed me up there?

Answer 18

yeap

Answer 19

\(\large \bf \sqrt[{\color{red}{ something}}]{x^{{\color{red}{ something}}}y^{{\color{red}{ something}}}}\iff xy\)

if the exponent of the radicand, matches the root, they come out, without their exponent

Answer 20

my answer choice then be -7x

Answer 21

bear in mind that the choices are just guidelines

the resultant value is -7x, yes

now if the choices are worth anything, they'd reflect that

Answer 22

Thank you :)