What is (m*m^{-2}n^{5/3})^2 ?

The solution to (m*m^{-2}n^{5/3})^2 is (n^{10/3})/(m^2)

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simplify (m*m^{-2}n^{5/3})^2

simplify

(m \cdot m^{- 2} n^{\frac{5}{3}})^{2}

\frac{n ^{\frac{10}{3}}}{m ^{2}}

Solution steps

(m m^{- 2} n^{\frac{5}{3}})^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(m m^{- 2} n^{\frac{5}{3}})^{2} = m^{2} (m^{- 2})^{2} (n^{\frac{5}{3}})^{2}

= m^{2} (m^{- 2})^{2} (n^{\frac{5}{3}})^{2}

Simplify

(m^{- 2})^{2} : \frac{1}{m ^{4}}

= m^{2} \frac{1}{m ^{4}} (n^{\frac{5}{3}})^{2}

Simplify

(n^{\frac{5}{3}})^{2} : n^{\frac{10}{3}}

= m^{2} \frac{1}{m ^{4}} n^{\frac{10}{3}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot m ^{2} n ^{\frac{10}{3}}}{m ^{4}}

Multiply:

1 \cdot m^{2} = m^{2}

= \frac{m ^{2} n ^{\frac{10}{3}}}{m ^{4}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{m ^{2}}{m ^{4}} = \frac{1}{m ^{4 - 2}}

= \frac{n ^{\frac{10}{3}}}{m ^{4 - 2}}

Subtract the numbers:

4 - 2 = 2

= \frac{n ^{\frac{10}{3}}}{m ^{2}}

15 x + 3 = 10 x + 3

\frac{a}{70} = \frac{70}{100}

x^{2} - 12 x + 36 = 90

6 (3)^{2}

3 n^{2} - 143 n + 1210 = 0

What is (m*m^{-2}n^{5/3})^2 ?
The solution to (m*m^{-2}n^{5/3})^2 is (n^{10/3})/(m^2)