Simplify the following, (3x^5y)^2(4x^3y^2)/2x^3y^-6

lina a

wrote...

4 years ago

Simplify the following, (3x^5y)^2(4x^3y^2)/2x^3y^-6

simplify

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bio_man

wrote...

Educator

4 years ago

hi lina a

Sorry for the late response.

I had a hard time decoding your equation. Take a look at the orange equation, is it the same as what is written in your question?

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lina a.

wrote...

4 years ago

Hi, its okay you were close except, the y isn't a exponent, its on its own, same thing with the other y, the y just has an exponent of 2, as well as the 3rd y which is on its own with an exponent of -6.

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bio_man

wrote...

Educator

4 years ago

Okay, I'll give it another go:

\(\frac{(3x^5y)^2(4x^3y^2)}{2x^3y^{-6}}\)

Distribute the exponent 2 into the first set of parentheses:

\(\frac{9x^{10}y^2\cdot (4x^3y^2)}{2x^3y^{-6}}\)

Multiply the factors 9 and 4 found in the numerator:

\(\frac{36x^{10}y^2(x^3y^2)}{2x^3y^{-6}}\)

Simplify the numerator further, and divide out 36/2 to get 18:

\(\frac{18x^{13}y^4}{x^3y^{-6}}\)

Use the quotient rule to combine the exponents:

\(18x^{10}y^{10}\) -- Simplified to its max.

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