Question

(5/b)^-3

Answer 1

thanks for sharing that

Answer 2

ok, start by rewriting what is inside the brackcts in index form

\[(\frac{5}{b})^{-3} = (5^1 \times b^{-1})^{-3}\]

does that make sense..?

Answer 3

ps... this is a little longer, just to explain it.

Answer 4

yeah but aren't you supposed to make the exponent positive?

Answer 5

hold on....

now the power operates on both terms so its

\[(5^1)^{-3} \times (b^{-1})^{-3}\]

and the power of a power law says multiply the powers

\[(x^a)^b = x^{a \times b}\]

you need to apply the law to this problem...

what would you get..?

Answer 6

\[\left(\frac{5}{b}\right)^{-3}\implies \left(\frac{b}{5}\right)^3=\frac{(b)^3}{(5)^3}=~?
\]

Answer 7

5b^3?

Answer 8

almost

\[(5^1)^{-3} = 5^{1 \times -3} = 5^{-3}\]

does that make sense..?

Answer 9

ohhh yeah i did it a different way i think, but i get it

Answer 10

so the problem is \[5^{-3} \times b^{-1 \times -3} = 5^{-3} b^3\]

negative powers are for fractions

then its \[5^{-3} \times b^3 = \frac{1}{5^3} \times b^3 = \frac{b^3}{5^3}\]

you may have to find the value of5^3

it depends on how the answer needs to be written.

@Jhannybean has written a correct solution

Answer 11

Just another method. No solution there yet :P

Answer 12

oh ok