The Power of a Power Rule

Simplify. All variables represent nonzero real numbers.

-5y^4(y^5)^2 / 15y^7(y^2)^3

I got:

-5y^40 / 15y^42

Is this correct?

no. In the numberator, y^5 squared is y^10. That times y^4 is y^14

In the denominator, y^2 cubed is y^6, and that times y^7 is y^13

then y^14/y^13 is y

Thanks. See my other post for a comment.

Wow... this is all the way from 2009 and I'm commenting on this in 2016. Really scary...

To simplify the given expression, you can apply the power of a power rule.

The power of a power rule states that when raising a power to another power, you multiply the exponents. In this case, we have:

(-5y^4(y^5)^2) / (15y^7(y^2)^3)

First, simplify the exponents of (y^5)^2 and (y^2)^3:

(y^5)^2 = y^(5*2) = y^10
(y^2)^3 = y^(2*3) = y^6

Now, substitute these simplified forms back into the expression:

(-5y^4 * y^10) / (15y^7 * y^6)

Next, simplify the multiplication of the variables by adding their exponents:

-5 * y^(4 + 10) / 15 * y^(7 + 6)

-5 * y^14 / 15 * y^13

Finally, divide the coefficients and subtract the exponents with the same base:

-1/3 * y^(14 - 13) = -1/3 * y^1 = -1/3y

Therefore, the simplified expression is -1/3y.

Your answer of -5y^40 / 15y^42 is not correct. Remember to simplify the exponents before performing any other operations.