Simplify. Rewrite the expression in the form 5^(n). (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. Base: 5 Exponent in numerator: 10 Exponent in denominator: 12Apply 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). 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. Calculation: 5^(-2) = 1/(5^2) = 1/25 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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Math Problems

Grade 8

Evaluate expressions using properties of exponents

Full solution

Q. Simplify.

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Rewrite the expression in the form

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5^{n}

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\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 $5^{-2}$ .