Question

5x^(-5)=1/32

Answer 1

@ganeshie8

Answer 2

@pooja195

Answer 3

@Michele_Laino

Answer 4

\[simplify \sqrt[5]{160}\to 2\sqrt[5]{5}\]

Answer 5

hint:
after a simplification, i can write this:
\[\Large \frac{5}{{{x^5}}} = \frac{1}{{{2^5}}}\]
since \(32=2^5\)

Answer 6

Switch sides\[x=2\sqrt[5]{5}\] <- your answer

Answer 7

hint:
if I take the inverse of both sides, I get:
\[\Large \frac{{{x^5}}}{5} = {2^5}\]
now, please multiply both sides by 5, what do you get?

Answer 8

idk... i was never taught exponents

Answer 9

@Michele_Laino ????

Answer 10

after the indicated multiplication, I get:
\[\huge {x^5} = 5 \cdot {2^5}\]
then I have to make the \(5-th\) rooth of both sides, so I can write:
\[\huge \sqrt[5]{{{x^5}}} = \sqrt[5]{5} \cdot \sqrt[5]{{{2^5}}}\]
now, please apply this rule to both sides:
\[\huge \sqrt[5]{{{a^m}}} = {a^{\frac{m}{5}}}\]
what do you get?

Answer 11

i still have no idea, i was never taught this stuff.

Answer 12

in particular, if \(m=5\), we can write this
\[\huge \begin{gathered}
\sqrt[5]{{{x^5}}} = {x^{\frac{5}{5}}} = {x^1} = x \hfill \\
\hfill \\
\sqrt[5]{{{2^5}}} = {2^{\frac{5}{5}}} = {2^1} = 2 \hfill \\
\end{gathered} \]

Answer 13

OMG! it all just worked out in my head. one question tho, why would m=5?

Answer 14

since I wrote a more general formula, and in order to solve your exercise, we need to replace \(m=5\)

Answer 15

ohhh okay. thank you SOOOO much!!

Answer 16

:)