Identify given equation: Identify the given equation and the base of the exponents. The equation is (5^(9))/(5^(x))=625, and the base for both exponents is 5.Simplify left side: Use the property of exponents that states (a^m)/(a^n) = a^(m-n) to simplify the left side of the equation. (5^(9))/(5^(x)) = 5^(9-x)Recognize power of 625: Recognize that 625 is a power of 5. Since 5^4 = 625, we can rewrite the equation as: 5^(9-x) = 5^4Set exponents equal: Since the bases are the same and the equation is an equality, the exponents must be equal. Set the exponents equal to each other: 9 - x = 4Solve for x: Solve for x by isolating it on one side of the equation. x = 9 - 4 x = 5

Resources

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$\frac{5^{9}}{5^{x}}=625$

View step-by-step help

Home

Math Problems

Precalculus

Operations with rational exponents

Full solution

\frac{5^{9}}{5^{x}}=625

Identify given equation: Identify the given equation and the base of the exponents. $\newline$ The equation is $(5^{9})/(5^{x})=625$ , and the base for both exponents is $5$ .
Simplify left side: Use the property of exponents that states $\frac{a^m}{a^n} = a^{m-n}$ to simplify the left side of the equation. $\frac{5^9}{5^x} = 5^{9-x}$
Recognize power of $625$ : Recognize that $625$ is a power of $5$ . Since $5^4 = 625$ , we can rewrite the equation as: $\newline$ $5^{9-x} = 5^4$
Set exponents equal: Since the bases are the same and the equation is an equality, the exponents must be equal. Set the exponents equal to each other: $9 - x = 4$
Solve for x: Solve for x by isolating it on one side of the equation. $\newline$ $x = 9 - 4$ $\newline$ $x = 5$