rewrite the expression with positive exponents and simplify

( – 3x^2)^5(9x^3)^–1

Question

rewrite the expression with positive exponents and simplify

( – 3x^2)^5(9x^3)^–1

mjdennis · Answer

$$(-3x ^{2})^{5} (9x ^{3})^{-1}$$Is that your starting point?

Do you understand what a negative exponent means? $$y^{-1} = \frac{ 1 }{ y }$$ and $$y ^{-2} = \frac{ 1 }{ y ^{2} }$$

hayley7 · Answer

yes i understand that the answer is -27x^7 i just don't understand how it is x^7 when i did it I got -27x^3

mjdennis · Answer

The coefficient -27 is correct.
Let's take that part to the front and see what is left of the original problem...$$-27 (x ^{5})^{2}(x ^{3})^{-1}$$  Any problems there?  Does that help you find what you did wrong?

hayley7 · Answer

yes thank you i was adding the exponents instead of multiplying

mjdennis · Answer

Sure.  just remember you multiply when an exponent works on another exponent, like (x^2)^5, and you add when the bases are multiplied (like x^2*x^5