Find out the answer to "Perform the indicated operations and simplify. 6x37y3×14x15y2×25y4x3"

EunoR

Answered question

2021-10-28

Perform the indicated operations and simplify.

\frac{6 x^{3}}{7 y^{3}} \times \frac{14 x}{15 y^{2}} \times \frac{25 y^{4}}{x^{3}}

avortarF

Skilled2021-10-29Added 113 answers

Step 1
Multiplication of fractions:
Fractions are multiplied as shown below.

\frac{a}{b} \times \frac{c}{d} = \frac{a c}{b d}

Step 2
Simplify the given expression as follows.

\frac{6 x^{3}}{7 y^{3}} \times \frac{14 x}{15 y^{2}} \times \frac{25 y^{4}}{x^{3}} = \frac{6 x^{3} \times 14 x \times 25 y^{4}}{7 y^{3} \times 15 y^{2} \times x^{3}}

= \frac{2100 x^{4} y^{4}}{105 x^{3} y^{5}}

= 20 x^{4 - 3} y^{4 - 5} (\frac{a^{m}}{a^{n}}) = a^{m - n}

= 20 x y^{- 1}

= \frac{20 x}{y}

Therefore, the given expression can be simplified as

= \frac{20 x}{y}

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