How do you simplify ${(\frac{- 7^{2} r^{5} s^{- 3}}{3^{- 1} r^{- 4} s^{4}})}^{4}$ $((-7^2 r^5 s^-3)/( 3^-1 r^-4 s^4))^4$ ?

Question

How do you simplify ${(\frac{- 7^{2} r^{5} s^{- 3}}{3^{- 1} r^{- 4} s^{4}})}^{4}$ $((-7^2 r^5 s^-3)/( 3^-1 r^-4 s^4))^4$ ?

1 Answer

Impact of this question

1812 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-11T23:04:44

$A = \frac{(147^{4}) \cdot r^{36}}{s^{28}}$ $A=((147^4)*r^36)/(s^28)$

Explanation:

Let's go to simplify : $A = {(\frac{- 7^{2} r^{5} s^{- 3}}{3^{- 1} r^{- 4} s^{4}})}^{4}$ $A=((-7^2r^5s^(-3))/(3^(-1)r^(-4)s^4))^4$

First, use this properties :
$\to$ $->$ $a^{- n} = \frac{1}{a^{n}}$ $color(red)(a^(-n) = 1/a^n)$
$\to$ $->$ $\frac{1}{a^{- n}} = a^{n}$ $color(red)(1/a^(-n) = a^n)$

$A = {(\frac{- 7^{2} \cdot 3^{1} r^{5} r^{4}}{s^{4} s^{3}})}^{4}$ $A=((-7^2*color(red)(3^1)r^5color(red)(r^4))/(s^4color(red)(s^3)))^4$

Second, simplify $A$ $A$ with that :

$a^{n} \cdot a^{m} = a^{n + m}$ $color(blue)(a^n*a^m=a^(n+m))$

$A = {(\frac{- 49 \cdot 3 \cdot r^{9}}{s^{7}})}^{4}$ $A=((-49*3*color(blue)(r^9))/(color(blue)(s^7)))^4$

Finally, apply the power $4$ $4$ to the fraction inside the parenthesis, with :

${(k \times a^{x})}^{y} = k^{y} \times a^{x \cdot y}$ $color(green)((kxxa^x)^y=k^yxxa^(x*y))$

$A = \frac{{(- 147)}^{4} \cdot r^{36}}{s^{28}}$ $A=((-147)^4*color(green)(r^36))/(color(green)(s^28))$

Therefore :

$A = \frac{466948881 \cdot r^{36}}{s^{28}}$ $A=(466948881*r^36)/(s^28)$

Science

Math

Humanities

... and beyond

How do you simplify ${(\frac{- 7^{2} r^{5} s^{- 3}}{3^{- 1} r^{- 4} s^{4}})}^{4}$ $((-7^2 r^5 s^-3)/( 3^-1 r^-4 s^4))^4$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you simplify (−72r5s−33−1r−4s4)4((-7^2 r^5 s^-3)/( 3^-1 r^-4 s^4))^4?

1 Answer

Explanation:

Related questions

Impact of this question

How do you simplify ${(\frac{- 7^{2} r^{5} s^{- 3}}{3^{- 1} r^{- 4} s^{4}})}^{4}$ $((-7^2 r^5 s^-3)/( 3^-1 r^-4 s^4))^4$ ?