0. Functions

Simplify the expression using exponent rules.

$\(\left\)(-5a^2\(\right\))\(\left\)(3a^8\(\right\))$

Simplify the expression using exponent rules.

$-\(\frac{12b^{11}\)}{4b^7}$

Rewrite the expression using exponent rules.

$\(\left\)(4x^2\(\right\))^3$

Rewrite the expression using exponent rules.

$\(\left\)(\(\frac{3x^4}{y^{-2}\)}\(\right\))^3$

Properties of exp(x) Use the inverse relations between ln x and exp(x), and the properties of ln x, to prove the following properties:

b. exp(x − y) = exp(x) / exp(y)

Properties of exp(x) Use the inverse relations between ln x and exp(x), and the properties of ln x, to prove the following properties:

c. (exp(x))ᵖ = exp(px), p rational

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. Assume x > 0 and y > 0.

d. 2ˣ = 2² ˡⁿ ˣ