Which expression is equivalent to (3^(-5)*3^(0))/(3^(-1))? 0 1 (1)/(3^(4)) (1)/(3^(2))

Simplify Exponents: Simplify the numerator using the properties of exponents. We have 3^(-5) * 3^(0). According to the properties of exponents, any number raised to the power of 0 is 1. So, 3^(0) = 1. Now, we multiply 3^(-5) by 1, which is just 3^(-5).Divide Exponents: Simplify the entire expression by dividing the numerator by the denominator. We have (3^(-5))/(3^(-1)). According to the properties of exponents, when we divide two expressions with the same base, we subtract the exponents. So, 3^(-5) / 3^(-1) = 3^(-5 - (-1)) = 3^(-5 + 1) = 3^(-4).Write Final Expression: Write the final simplified expression. The expression 3^(-4) can be written as 1/(3^(4)) because any negative exponent indicates that the base is on the bottom of a fraction raised to the positive of that exponent. So, the equivalent expression is 1/(3^(4)).

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Which expression is equivalent to
(3^(-5)*3^(0))/(3^(-1))?
0
1

(1)/(3^(4))

(1)/(3^(2))

Which expression is equivalent to $\frac{3^{-5} \cdot 3^{0}}{3^{-1}} ?$ $\newline$ $0$ $\newline$ $1$ $\newline$ $\frac{1}{3^{4}}$ $\newline$ $\frac{1}{3^{2}}$

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Algebra 1

Multiplication with rational exponents

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Q. Which expression is equivalent to

\frac{3^{-5} \cdot 3^{0}}{3^{-1}} ?

\newline

0

\newline

1

\newline

\frac{1}{3^{4}}

\newline

\frac{1}{3^{2}}

Simplify Exponents: Simplify the numerator using the properties of exponents. $\newline$ We have $3^{-5} \times 3^{0}$ . According to the properties of exponents, any number raised to the power of $0$ is $1$ . So, $3^{0} = 1$ . $\newline$ Now, we multiply $3^{-5}$ by $1$ , which is just $3^{-5}$ .
Divide Exponents: Simplify the entire expression by dividing the numerator by the denominator. $\newline$ We have $(3^{-5})/(3^{-1})$ . According to the properties of exponents, when we divide two expressions with the same base, we subtract the exponents. $\newline$ So, $3^{-5} / 3^{-1} = 3^{-5 - (-1)} = 3^{-5 + 1} = 3^{-4}$ .
Write Final Expression: Write the final simplified expression. $\newline$ The expression $3^{-4}$ can be written as $1/(3^{4})$ because any negative exponent indicates that the base is on the bottom of a fraction raised to the positive of that exponent. $\newline$ So, the equivalent expression is $1/(3^{4})$ .