Question

What is the simplified form of each expression? (3x^7/2)^6(x^2)^6

Answer 1

\(\large \bf (3x^{\frac{7}{2}})^{\color{red}{ 6}}(x^2)^{\color{red}{ 2}}\implies 3^{\color{red}{ 6}}x^{\frac{7}{2}\cdot {\color{red}{ 6}}}\cdot x^{2\cdot {\color{red}{ 2}}}\implies 3^{\color{red}{ 6}}x^{\frac{7}{2}\cdot {\color{red}{ 6}}+2\cdot {\color{red}{ 2}}}\)

Answer 2

so... 729 times x^21+4? am I on the right track?

Answer 3

so... 729 times x^21+4? am I on the right track? \(\large \checkmark\)

notice that, when in a parentheses, you distribute the exponent

and when you have the same base, but different exponent
you keep the base, SUM the exponents

Answer 4

Okay 729x^21+4?
That cant be right... O.o

Answer 5

well, heheh, it's if it's \(\Large \bf (3x^{\frac{7}{2}})^{\color{red}{ 6}}(x^2)^{\color{red}{ 2}}\)

Answer 6

unless you mistyped it or missed something

Answer 7

shouldn't the ^2 be times by 6 instead of 2? cause none of my answers say 729x^25

Answer 8

ahemm no, because the ^2 is an exponent of ANOTHER component, while the ^6 is elsewhere

they only merge because the BASE is the same

Answer 9

but in the beginning of the problem it says (x^2)^6. im not trying to be a pain I just really need to figure this out... :/

Answer 10

hmmm that's not what you have originally \(\huge \bf (3x^{\frac{7}{2}})^{\color{red}{ 6}}(x^2)^{\color{red}{ 2}}\)

Answer 11

(3x^7/2)^6(x^2)^6 see that's our mix up

Answer 12

\(\huge (3x^{^{\frac{7}{2}})^{\color{red}{ 6}}}(x^2)^{\color{red}{ 2}}\) tis what I read

Answer 13

well. same procedure, do the same, distribute the exponent
same bases, keep the base, add the exponents

Answer 14

okay so the answer would be 729x^33?

Answer 15

okay so the answer would be 729x^33? \(\large \checkmark\)

Answer 16

Okay thank you!

Answer 17

yw