Write without negative exponents (3x^2 y^-3)^-5?

[(3x^2)/(y^3)] ^ - 5

1 / [(3x^2)/(y^3)] ^5

using your exponent property to distribute the exponent
1/[ (3^5x^10)/y^15]

y^15
------
243x^10

remember anything to a negative exponent a^-1 is 1/a^1 - one over the variable to the positive of the original exponent

and the exponent rule used (a^n)^m = a^(n*m)

y^15 / [(3^5)(x^10)]

(2x^-3y^4)^-3 (distribute the exponent) (2)^-3x^9y^-12 (circulate the damaging exponents to the denominator to lead them to helpful) x^9/(2^3y^12) x^9/(8y^12) <===answer once you prepare an exponent to a diverse exponent, you multiply the powers, like (x^2)^3 = x^(2*3) = x^6. to alter a damaging exponent to an excellent exponent, you progression it from the numerator to the denominator or from the denominator to the numerator. And once you stated "in this situation each and all the squared 3's are damaging," i think of you meant each and all the exponents of three are damaging, on account that "sq." skill rather to the capacity of two.

(3x^2y^-3)^-5
= (3^-5)(x^2)^-5(y^-3)^-5
= [1/3^5][x^(2 * -5)][y^(-3 * -5)]
= [1/243][x^-10][y^15]
= [1/243][1/x^10][y^15]
= y^15/243x^10

Negative exponents can be converted to positive if the base is in the denominator of a fraction:
(3x^2 y^-3)^-5=1/(3x^2 y^-3)^5

Negative exponents just mean it goes in the denominator if it's in the numerator, or reverse if the negative exponent is in the denominator already.

So, first, you have a -5 exponent that you want to bring down to the denominator to make it positive.

(3x^2 * y^-3)^-5

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

Now, there is a -3 in there, but you cannot make it positive yet. You first have to distribute the 5. When you have an exponent and take it to another power, you multiply the two powers together.

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

1/[(3^5*x^(2*5) * y^(-3*5)]

1/[243x^10 * y^-15]

Now we can bring y^-15 to the top to make it positive.

1/[243x^10 * y^-15]

y^15 / [243x^10]

I hope that helps!

(1)/(243x^10*y^3).

Just take the expression to the fifth power, and put it under 1. Negative exponents mean fractions.

Then (3X^2/Y^3)^ -5 1/(3X^2/ Y^3)^ -5 =(Y^3/ 3X ^2)^ +5 =
= Y^+15 / 243X^ +10

Writting fractions is not easy here; so I hope it is clear enough:

1 / (3x^2 / y^3)^5

Negative exponents can be converted to positive if the base is in the denominator of a fraction:

x^-2 = 1 / x^2

[y^3/3x^2]^5