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