simplify. express answer with positive exponents only. (-2x^-5y^4z^2)-3

(-2x^-5y^4z^2)^-3

multiply all the exponents by -3 to get

-2^-3 x^15 y^-12 z^-6
-x^15/(8 y^12 z^6)

Xto the 5th power next to Xto the negative 3 power?

(3xy-2)2

x3

To simplify the expression (-2x^-5y^4z^2)^-3 and express the answer with positive exponents only, we can apply the rule of negative exponents. The rule states that if we have a negative exponent, we can move the term with the negative exponent to the denominator and change the sign of the exponent to positive.

First, let's simplify the base with the negative exponents:

-2x^-5y^4z^2

To remove the negative exponent on x^-5, we move x^-5 to the denominator as x^5:

-2y^4z^2 / (x^5)

Next, we raise the expression to the power of -3:

((-2y^4z^2) / (x^5))^-3

To do this, we invert the entire expression and change the sign of the exponent:

1 / ((-2y^4z^2) / (x^5))^3

Next, let's simplify the exponent inside the parentheses. Raising a fraction to a power means raising the numerator and the denominator to that power:

1 / (-2y^4z^2)^3 / (x^5)^3

Simplifying further:

1 / (-8y^12z^6) / (x^15)

Applying the rule of negative exponents again, we can move the negative exponent back to the numerator:

1 / (x^15 / (-8y^12z^6))

Finally, since dividing by a fraction is the same as multiplying by its reciprocal, we can rewrite the expression:

1 * (-8y^12z^6 / x^15)

Simplifying further:

-8y^12z^6 / x^15

Therefore, the simplified expression (-2x^-5y^4z^2)^-3 expressed with positive exponents only is -8y^12z^6 / x^15.