Chapter 4, Problem 1CCE

State as many laws of exponents as you can recall.

To determine

Laws of exponents.

Answer to Problem 1CCE

Solution:

1) Product rule: $b^x\cdot b^y=b^{x+y}$

2) Changing the sign of exponents: $b^{-x}=\frac{1}{b^x}$

3) Quotient rule: $\frac{b^x}{b^y}=b^x\cdot b^{-y}=b^{x-y}$

4) Power of a power: ${\left(b^y\right)}^x=b^{xy}$

5) Power of a product: $a^x{b}^x={\left(ab\right)}^x$

6) Power of a quotient: $\frac{a^x}{b^x}={\left(\frac{a}{b}\right)}^x$

Explanation of Solution

Given information:

Instruction to describe thelaws of exponents.

Explanation:

The function $f(x)=b^x$ is called an exponential function since the variable $x$ is in the exponent.

The number $b$ is a base of the exponential function.

Laws of Exponents are below:

1) Product rule: $b^x\cdot b^y=b^{x+y}$

2) Changing the sign of exponents: $b^{-x}=\frac{1}{b^x}$

3) Quotient rule: $\frac{b^x}{b^y}=b^x\cdot b^{-y}=b^{x-y}$

4) Power of a power: ${\left(b^y\right)}^x=b^{xy}$

5) Power of a product: $a^x{b}^x={\left(ab\right)}^x$

6) Power of a quotient: $\frac{a^x}{b^x}={\left(\frac{a}{b}\right)}^x$