Math 22 Exponential Functions

Definition of Exponential Function

 If Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a>0}
 and $a\neq 1$, then the exponential function with base $a$ is $a^{x}$

Properties of Exponents

Let $a$ and $b$ be positive real numbers, and let $x$ and $y$ be real numbers.

1.$a^{0}=1$

2.$a^{x}a^{y}=a^{x+y}$

3.${\frac {a^{x}}{a^{y}}}=a^{x-y}$

4.$(a^{x})^{y}=a^{xy}$

5.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (ab)^x=a^xb^x}

6.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (\frac{a}{b})^x=\frac{a^x}{b^x}}

7.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a^{-x}=\frac{1}{a^x}}

Exercises Use the properties of exponents to simplify each expression:

a) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (8^{\frac{1}{2}})(2^{\frac{1}{2}})}

Solution:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (8^{\frac{1}{2}})(2^{\frac{1}{2}})=(8\cdot 2)^{\frac{1}{2}}=16^{\frac{1}{2}}}

b) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{7^5}{49^3}}

Solution:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{7^5}{49^3}=\frac{7^5}{(7^2)^3}=\frac{7^5}{7^{2.3}}=\frac{7^5}{7^6}=7^{5-6}=7^{-1}=\frac{1}{7}}

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