Which expressions are equivalent to the one below? Check all that apply. 9^x
f. x^5
\(a.\ 9\cdot9^{x+1}=9^{1+x+1}=9^{x+2}
eq9^x\\\\b.\ \left(\frac{36}{4}\right)^x=9^x\ OK\ :)\\\\c.\ \frac{36^x}{4}
eq9^x\\\\d.\ 9\cdot9^{x-1}=9^{1+x-1}=9^x\ \ OK\ :)\\\\e.\ \frac{36^x}{4^x}=\left(\frac{36}{4}\right)^x=9^x\ \ \ OK\ :)\\\\f.\ x^5
eq9^x\\\\Answer:\huge\boxed{b;\ d;\ e}\)
\(Used:\\\\a^n\cdot a^m=a^{n+m}\\\\\frac{a^n}{b^n}=\left(\frac{a}{b}\right)^n\)
In between given 6 exponential expressions, \((\frac{36}{4} )^{x}\), 9 × \(9^{x - 1}\), and \(\frac{36^{x}}{4^{x}}\) are equivalent to \(9^{x}\)
"An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable."
Given expression is \(9^{x}\).
a. 9 × \(9^{x + 1}\) is equal to \(9^{x + 2}\).
b. \((\frac{36}{4} )^{x}\) is equal to \(9^{x}\).
c. \(\frac{36^{x}}{4}\) is equal to \(9^{x}\) × \(4^{x - 1}\).
d. 9 × \(9^{x - 1}\) is equal to \(9^{x}\).
e. \(\frac{36^{x}}{4^{x}}\) is equal to \(9^{x}\).
f. \(x^{5}\) is equal to \(x^{5}\) .
Therefore, from the given expressions, \((\frac{36}{4} )^{x}\), 9 × \(9^{x - 1}\), and \(\frac{36^{x}}{4^{x}}\) are equivalent to \(9^{x}\).
Learn more about an exponential expression here: https://brainly.com/question/11471525
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