Question

simply the expression. write your answers using only positive exponents.

Answer 1

We can apply the exponent rules to solve this problems.

2) In this case we have to convert the negative exponent into a positive exponent. We can do it like this:

$y^{-5}=\frac{1}{y^5}$

3) In this case we applied the same rule as in (2) for the y exponent:

$9x^6y^{-3}=9x^6\cdot\frac{1}{y^3}=\frac{9x^6}{y^3}$

4) In this case, we can simplify the expression as:

$\frac{5^6}{5}=\frac{5^6}{5^1}=5^6\cdot5^{-1}=5^{6-1}=5^5=3125$

5) We apply the product rule:

$4^{-3}\cdot4^5=4^{-3+5}=4^2=16$

6) We apply the power rule:

$(w^5)^7=w^{5\cdot7}=w^{35}$

7) We can simplify this as:

$(-5z)^3=(-5)^3\cdot z^3=-125z^3$