What is (1/2 k^2w^2z^3)(5/3 k^2w^2z)(4/3 wz) ?

The solution to (1/2 k^2w^2z^3)(5/3 k^2w^2z)(4/3 wz) is (10k^4w^5z^5)/9

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simplify (1/2 k^2w^2z^3)(5/3 k^2w^2z)(4/3 wz)

simplify

(\frac{1}{2} k^{2} w^{2} z^{3}) (\frac{5}{3} k^{2} w^{2} z) (\frac{4}{3} w z)

\frac{10 k ^{4} w ^{5} z ^{5}}{9}

Solution steps

(\frac{1}{2} k^{2} w^{2} z^{3}) (\frac{5}{3} k^{2} w^{2} z) (\frac{4}{3} w z)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

k^{2} k^{2} = k^{2 + 2}

= \frac{1}{2} w^{2} z^{3} \frac{5}{3} k^{2 + 2} w^{2} z \frac{4}{3} w z

Add the numbers:

2 + 2 = 4

= \frac{1}{2} w^{2} z^{3} \frac{5}{3} k^{4} w^{2} z \frac{4}{3} w z

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

w^{2} w^{2} w = w^{2 + 2 + 1}

= \frac{1}{2} z^{3} \frac{5}{3} k^{4} z \frac{4}{3} w^{2 + 2 + 1} z

Add the numbers:

2 + 2 + 1 = 5

= \frac{1}{2} z^{3} \frac{5}{3} k^{4} z \frac{4}{3} w^{5} z

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

z^{3} zz = z^{3 + 1 + 1}

= \frac{1}{2} \cdot \frac{5}{3} k^{4} \frac{4}{3} w^{5} z^{3 + 1 + 1}

Add the numbers:

3 + 1 + 1 = 5

= \frac{1}{2} \cdot \frac{5}{3} k^{4} \frac{4}{3} w^{5} z^{5}

Multiply fractions:

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

= \frac{1 \cdot 5 \cdot 4 k ^{4} w ^{5} z ^{5}}{2 \cdot 3 \cdot 3}

Refine

= \frac{20 k ^{4} w ^{5} z ^{5}}{18}

Cancel the common factor:

2

= \frac{10 k ^{4} w ^{5} z ^{5}}{9}

3.28 \cdot 1 0^{- 6}

e^{- \frac{t}{2}} \cdot e^{- s t}

275500 (1 + \frac{0.11}{2})^{- 10} (1 + 0.11 (\frac{11}{12}))

\frac{x - 2}{5 - x}

\frac{x - 1}{x ^{2} - 5 x + 6}

What is (1/2 k^2w^2z^3)(5/3 k^2w^2z)(4/3 wz) ?
The solution to (1/2 k^2w^2z^3)(5/3 k^2w^2z)(4/3 wz) is (10k^4w^5z^5)/9