Question

5-72. rewrite each expression in the form $a(b)^x$. homework help a. $5^{2x}$ b. $3^{2x - 3}$

Explanation:

Step1: Apply exponent power rule

Recall $(x^m)^n = x^{mn}$. For $5^{2x}$, rewrite as $(5^2)^x$.
$5^{2x} = (5^2)^x = 25^x = 1(25)^x$

Step2: Split exponent using quotient rule

Recall $x^{m-n} = \frac{x^m}{x^n}$. For $3^{2x-3}$, split into $\frac{3^{2x}}{3^3}$.
$3^{2x-3} = \frac{3^{2x}}{3^3}$

Step3: Simplify base and constant

Simplify $3^3=27$, and rewrite $3^{2x}=(3^2)^x=9^x$.
$\frac{3^{2x}}{3^3} = \frac{9^x}{27} = \frac{1}{27}(9)^x$

Answer:

a. $1(25)^x$
b. $\frac{1}{27}(9)^x$