What is 5c^{-7}d^2*(-cd^2)^4 ?

The solution to 5c^{-7}d^2*(-cd^2)^4 is (5d^{10})/(c^3)

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simplify 5c^{-7}d^2*(-cd^2)^4

simplify

5 c^{- 7} d^{2} \cdot (- c d^{2})^{4}

\frac{5 d ^{10}}{c ^{3}}

Solution steps

5 c^{- 7} d^{2} (- c d^{2})^{4}

Apply exponent rule:

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

c^{- 7} = \frac{1}{c ^{7}}

= 5 \cdot \frac{1}{c ^{7}} d^{2} (- c d^{2})^{4}

Simplify

(- c d^{2})^{4} : c^{4} d^{8}

= 5 \cdot \frac{1}{c ^{7}} d^{2} c^{4} d^{8}

Simplify

d^{2} d^{8} : d^{10}

= 5 \cdot \frac{1}{c ^{7}} d^{10} c^{4}

= 5 d^{10} c^{4} \frac{1}{c ^{7}}

Apply the fraction rule:

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

= \frac{5 d ^{10} c ^{4} \cdot 1}{c ^{7}}

Multiply the numbers:

5 \cdot 1 = 5

= \frac{5 d ^{10} c ^{4}}{c ^{7}}

Simplify

\frac{c ^{4}}{c ^{7}} : \frac{1}{c ^{3}}

= \frac{5 d ^{10}}{c ^{3}}

(s + 1) (s + 3)

\frac{- 4}{- 4}

(10 - 5 i) (- 8 - 8 i)

(2 - 5 y) (y^{2} + 6 y + 9)

g^{- 1} (x)

What is 5c^{-7}d^2*(-cd^2)^4 ?
The solution to 5c^{-7}d^2*(-cd^2)^4 is (5d^{10})/(c^3)