How do you simplify $\frac{{(m^{2})}^{2} z^{3} z d}{m z^{5} d^{3}}$ $((m^2)^2z^3zd)/(mz^5d^3)$ ?

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Answer 1 · 2017-02-01T01:37:15

$\frac{m^{3}}{z d^{2}}$ $(m^3)/(zd^2)$

Simplify $\frac{{(m^{2})}^{2} z^{3} z d}{m z^{5} d^{3}}$ $((m^2)^2z^3zd)/(mz^5d^3)$ .

First apply power rule ${(b^{m})}^{n} = b^{m \cdot n}$ $(b^m)^n=b^(m*n)$ .

$\frac{m^{(2 \cdot 2)} z^{3} z d}{m z^{5} d^{3}}$ $(m^((2*2))z^3zd)/(mz^5d^3)$

$\frac{m^{4} z^{3} z d}{m z^{5} d^{3}}$ $(m^4z^3zd)/(mz^5d^3)$

Apply product rule $a^{m} a^{n} = a^{(m + n)} .$ $a^ma^n=a^((m+n)).$
(Reminder: $b = b^{1}$ $b=b^1$ ).

$\frac{m^{4} z^{3} z^{1} d}{m z^{5} d^{3}}$ $(m^4z^3z^1d)/(mz^5d^3)$

$\frac{m^{4} z^{(3 + 1)} d}{m z^{5} d^{3}}$ $(m^4z^((3+1))d)/(mz^5d^3)$

Simplify.

$\frac{m^{4} z^{4} d}{m z^{5} d^{3}}$ $(m^4z^4d)/(mz^5d^3)$

Apply quotient rule $\frac{a^{m}}{a^{n}} = a^{(m - n)}$ $a^m/a^n=a^((m-n))$ .

$m^{(4 - 1)} z^{(4 - 5)} d^{(1 - 3)}$ $m^((4-1))z^((4-5))d^((1-3))$

Simplify.

$m^{3} z^{- 1} d^{- 2}$ $m^3z^(-1)d^(-2)$

Apply negative exponent rule $a^{- m} = \frac{1}{a^{m}}$ $a^(-m)=1/a^m$ .

$\frac{m^{3}}{z d^{2}}$ $(m^3)/(zd^2)$

How do you simplify ((m^2)^2z^3zd)/(mz^5d^3)(m2)2z3zdmz5d3((m^2)^2z^3zd)/(mz^5d^3)?