Answer to Question #171300 in Algebra for gibson

Question

simplify the following

1. 3²3⁴3^-5
2. (7⁰/7²)^-1
3. (2x³y⁴/xy⁷)²
4. (-2x²y³)³
5. (81/100)^-3/2
6. (-8)^2/3
7. (x^-1-y^-1)/(x-y)^-1

Answer 1

1.

$$3^23^43^{-5}=3^{2+4-5}=3$$

2.

$$(7^0/7^2)^{-1}=7^{-2(-1)}=49$$

3.

$$(2x^3y^4/xy^7)^2=(\dfrac{2x^2}{y^3})^2=\dfrac{4x^4}{y^6}$$

4.

$$(-2x^2y^3)^3=-8x^6y^9$$

5.

$$(81/100)^{-3/2}=\dfrac{(100^{1/2})^3}{(81^{1/2})^3}=\dfrac{1000}{729}$$

6.

$$(-8)^{2/3}=(64)^{1/3}=4$$

7.

$$(x^{-1}-y^{-1})/(x-y)^{-1}=(\dfrac{1}{x}-\dfrac{1}{y})(x-y)$$

$$=-\dfrac{(x-y)^2}{xy}$$