Which expression is equivalent to (3^(4))/(3^(5))*3^(8)? 3^(7) (1)/(3^(7)) 3^(9) (1)/(3^(9))

Simplify Expression: Simplify the expression using the properties of exponents. We have the expression (3^(4))/(3^(5))*3^(8). According to the properties of exponents, when we divide two expressions with the same base, we subtract the exponents. When we multiply two expressions with the same base, we add the exponents.Division Property: Apply the division property of exponents. (3^(4))/(3^(5)) = 3^(4-5) = 3^(-1)Multiplication Property: Apply the multiplication property of exponents. 3^(-1) * 3^(8) = 3^(-1+8) = 3^(7)Check Final Expression: Check the final expression against the given options. The simplified expression is 3^(7), which matches one of the given options.

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Which expression is equivalent to
(3^(4))/(3^(5))*3^(8)?

3^(7)

(1)/(3^(7))

3^(9)

(1)/(3^(9))

Which expression is equivalent to $\frac{3^{4}}{3^{5}} \cdot 3^{8} ?$ $\newline$ $3^{7}$ $\newline$ $\frac{1}{3^{7}}$ $\newline$ $3^{9}$ $\newline$ $\frac{1}{3^{9}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

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Q. Which expression is equivalent to

\frac{3^{4}}{3^{5}} \cdot 3^{8} ?

\newline

3^{7}

\newline

\frac{1}{3^{7}}

\newline

3^{9}

\newline

\frac{1}{3^{9}}

Simplify Expression: Simplify the expression using the properties of exponents. $\newline$ We have the expression $(3^{4})/(3^{5})\cdot3^{8}$ . According to the properties of exponents, when we divide two expressions with the same base, we subtract the exponents. When we multiply two expressions with the same base, we add the exponents.
Division Property: Apply the division property of exponents. $\newline$ $(3^{4})/(3^{5}) = 3^{4-5} = 3^{-1}$
Multiplication Property: Apply the multiplication property of exponents. $3^{-1} \times 3^{8} = 3^{-1+8} = 3^{7}$
Check Final Expression: Check the final expression against the given options. $\newline$ The simplified expression is $3^{7}$ , which matches one of the given options.