How do you simplify $(\frac{c^{2} d^{2}}{c d^{3}}) \cdot {(\frac{d^{2}}{c^{2}})}^{3}$ $((c^2d^2 )/ (cd^3)) * (d^2 / c^2)^3$ leaving only positive exponents?

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Answer 1 · 2018-03-15T16:14:27

$(\frac{c^{2} d^{2}}{c d^{3}}) \cdot {(\frac{d^{2}}{c^{2}})}^{3} = \frac{d^{5}}{c^{5}}$ $((c^2d^2)/(cd^3))*((d^2)/(c^2))^3=color(blue)(d^5/c^5$

Simplify.

$(\frac{c^{2} d^{2}}{c d^{3}}) \cdot {(\frac{d^{2}}{c^{2}})}^{3}$ $((c^2d^2)/(cd^3))*((d^2)/(c^2))^3$

Apply power rule of exponents: ${(a^{m})}^{n} = a^{m \cdot n}$ $(a^m)^n=a^(m*n)$

$(\frac{c^{2} d^{2}}{c d^{3}}) \cdot (\frac{d^{(2 \cdot 3)}}{c^{(2 \cdot 3)}})$ $((c^2d^2)/(cd^3))*(d^((2*3))/(c^((2*3))))$

Simplify.

$(\frac{c^{2} d^{2}}{c d^{3}}) \cdot (\frac{d^{6}}{c^{6}})$ $((c^2d^2)/(cd^3))*((d^6)/(c^6))$

Remove parentheses.

$\frac{c^{2} d^{2}}{c d^{3}} \cdot \frac{d^{6}}{c^{6}}$ $(c^2d^2)/(cd^3)*(d^6)/(c^6)$

Apply product rule of exponents: $a^{m} a^{n} = a^{m + n}$ $a^ma^n=a^(m+n)$

No exponent is understood to be an exponent of $1$ $1$ .

$\frac{c^{2} d^{(2 + 6)}}{c^{(1 + 6)} d^{3}}$ $(c^2d^((2+6)))/(c^((1+6))d^3)$

Simplify.

$\frac{c^{2} d^{8}}{c^{7} d^{3}}$ $(c^2d^8)/(c^7d^3)$

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

$c^{(2 - 7)} d^{(8 - 3)}$ $c^((2-7))d^((8-3))$

Simplify.

$c^{- 5} d^{5}$ $c^(-5)d^5$

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

$\frac{d^{5}}{c^{5}}$ $d^5/c^5$

How do you simplify ((c^2d^2 )/ (cd^3)) * (d^2 / c^2)^3(c2d2cd3)⋅(d2c2)3((c^2d^2 )/ (cd^3)) * (d^2 / c^2)^3 leaving only positive exponents?