3.1.6 Exponent Rules

These problems are usually on the third column, and if you know the basics of exponential rules they are easy to figure out. The rules to remember are as followed:

• $x^a \cdot x^b = x^{a+b}$
• $\frac{x^a}{x^b} = x^{a-b}$
• $(x^a)^b = x^{ab}$

The following are problems concerning each type:

Product Rule: Let $3^x = 70.1$, then $3^{x+2} = ?$ Solution: $3^{x+2} = 3^x \cdot 3^2 = 70.1 \cdot 9 = 630.9$

Quotient Rule: Let $5^x = 2$, represent $5^{x-2}$ as a decimal. Solution: $5^{x-2} = \frac{5^x}{5^2} = \frac{2}{25} = .08$

Power Rule: Let $4^x = 1.1$ then $2^{6x} = ?$ Solution: $4^x = 2^{2x} = 1.1 \Rightarrow 2^{6x} = (2^{2x})^3 = 1.1^3 = 1.331$

The following are some more problems about exponent rules:

Problem Set 3.1.6