Solutions

1.

Write each expression in the form b^r:

(a)

6^1/36^3/5 = 6^14/15.

(b)

(1/3)⁶(3/2)⁶=(1/2)⁶.

(c)

6^1/36^-3/5 = 6^-4/15.

(d)

$\left(6^{1/3}\right)^{-3/5}=6^{-1/5}$.

(e)

3^1/35^1/3 = 15^1/3.

2.

Combine exponents where possible.

(a)

(a²b³)⁵ = a¹⁰b¹⁵.

(b)

(a²b^-1)³(a² + b³) = a⁸b^-3 + a⁶.

(c)

$${\frac{(x^3y^2z^{-3})^2}{(xy^2z^3)^2} = x^4z^{-12}}$$.

(d)

$${ \frac{(x^{1/3}y^2z^{-3})^2}{(xy^{-1/2}z^3)^2}=x^{-4/3}y^5z^{-12}}$$.

(e)

$${\frac{(x^{-1}y^2z^{-1/3})^5}{(x^{-1}y^2z^3)^{1/7}} = x^{-34/7}y^{68/7}z^{-44/21}}$$.