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Simplify.
Rewrite the expression in the form
5^(n).

(5^(10))/(5^(12))=

Simplify. $\newline$ Rewrite the expression in the form $\newline$ $5^{n}$ . $\newline$ $\frac{5^{10}}{5^{12}}=$

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Evaluate expressions using properties of exponents

Full solution

Q. Simplify.

\newline

Rewrite the expression in the form

\newline

5^{n}

.

\newline

\frac{5^{10}}{5^{12}}=

Identify base and exponents: Identify the base and the exponents of both the numerator and the denominator. In $(5^{10})/(5^{12})$ , $5$ is the base raised to the exponent $10$ in the numerator and to the exponent $12$ in the denominator. $\newline$ Base: $5$ $\newline$ Exponent in numerator: $10$ $\newline$ Exponent in denominator: $12$
Apply quotient rule for exponents: Apply the quotient rule for exponents which states that when dividing like bases, you subtract the exponents. Rewrite $(5^{10})/(5^{12})$ as $5^{10 - 12}$ . $\newline$ Calculation: $5^{10 - 12} = 5^{-2}$
Simplify expression: Simplify the expression $5^{-2}$ to its simplest form. Since the exponent is negative, it indicates the reciprocal of the base raised to the positive exponent. $\newline$ Calculation: $5^{-2} = \frac{1}{5^2} = \frac{1}{25}$ $\newline$ However, the question prompt asks for the expression in the form $5^{n}$ , so we keep the expression as $5^{-2}$ .

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