We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# ((m^-3)(n^2)^-4)/((m^2)(n^-3))^2

0
551
2

((m^-3)(n^2)^-4)/((m^2)(n^-3))^2

A quick question, how do you get (m^8/n^2) out of this? I have no idea what to approach where. It's a little infuriating.

May 7, 2017

### 2+0 Answers

#1
+1

Simplify the following:
(1)/(((n^2)/(m^3))^4 ((m^2)/(n^3))^2)

Multiply each exponent in m^2/n^3 by 2:
(1)/((n^2/m^3)^4 (m^(2×2))/((n^3)^2))

2×2 = 4:
(1)/((n^2/m^3)^4 m^4/(n^3)^2)

Multiply exponents. (n^3)^2 = n^(3×2):
(1)/((n^2/m^3)^4 m^4/n^(3×2))

3×2 = 6:
(1)/((n^2/m^3)^4 m^4/n^6)

(n^2/m^3)^(-4) = (m^3/n^2)^4:
((m^3/n^2)^4)/(m^4/n^6)

Multiply each exponent in m^3/n^2 by 4:
((m^(4×3))/((n^2)^4))/(m^4/n^6)

4×3 = 12:
(m^12/(n^2)^4)/(m^4/n^6)

Multiply exponents. (n^2)^4 = n^(2×4):
(m^12/n^(2×4))/(m^4/n^6)

2×4 = 8:
(m^12/n^8)/(m^4/n^6)

Multiply the numerator by the reciprocal of the denominator, (m^12/n^8)/(m^4/n^6) = m^12/n^8×n^6/m^4:
(m^12 n^6)/(n^8 m^4)

Combine powers. (m^12 n^6)/(n^8 m^4) = m^(12 - 4) n^(6 - 8):
m^12 - 4 n^6 - 8

12 - 4 = 8:
m^8 n^(6 - 8)

6 - 8 = -2:
Answer: | m^8 n^-2

May 7, 2017
#2
+8108
+4

This might be a little bit easier to see :)

$$\large \frac{(m^{-3}n^2)^{-4}}{(m^2n^{-3})^2} \\~\\ =\frac{m^{12}n^{-8}}{m^4n^{-6}} \\~\\ =m^{12-4}n^{-8--6} \\~\\ =m^{8}n^{-2} \\~\\ =\frac{m^{8}}{n^{2}}$$

.
May 7, 2017