Simplify. (9)/(9^(-4//5))

Understand the problem: Understand the problem. We need to simplify the expression (9)/(9^(-4/5)).Apply exponent property: Apply the property of exponents that states a^(-n) = 1/(a^n). So, 9^(-4/5) is the same as 1/(9^(4/5)).Rewrite expression: Rewrite the original expression using the property from Step 2. (9)/(9^(-4/5)) becomes (9) * (9^(4/5)).Combine exponents: Apply the property of exponents that states a^(m) * a^(n) = a^(m+n). Combine the exponents of 9 by adding them together. Since the base is the same (9), we add the exponents: 1 + 4/5 = 5/5 + 4/5 = 9/5.Write with combined exponent: Write the expression with the combined exponent. The expression now is 9^(9/5).Simplify the expression: Simplify the expression. 9 is 3^2, so we can rewrite 9^(9/5) as (3^2)^(9/5).Apply exponent property: Apply the property of exponents that states (a^m)^n = a^(m*n). Multiply the exponents: 2 * (9/5) = 18/5.Write final expression: Write the final expression. The simplified form is 3^(18/5).

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Simplify. $\newline$ $\frac{9}{9^{-4 / 5}}$

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Math Problems

Algebra 1

Evaluate integers raised to rational exponents

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Q. Simplify.

\newline

\frac{9}{9^{-4 / 5}}

Understand the problem: Understand the problem. $\newline$ We need to simplify the expression $(9)/(9^{-4/5})$ .
Apply exponent property: Apply the property of exponents that states $a^{-n} = \frac{1}{a^n}$ . So, $9^{-\frac{4}{5}}$ is the same as $\frac{1}{9^{\frac{4}{5}}}$ .
Rewrite expression: Rewrite the original expression using the property from Step $2$ . $\newline$ $(9)/(9^{-4/5})$ becomes $(9) \times (9^{4/5})$ .
Combine exponents: Apply the property of exponents that states $a^{m} \cdot a^{n} = a^{m+n}$ . Combine the exponents of $9$ by adding them together. Since the base is the same ( $9$ ), we add the exponents: $1 + \frac{4}{5} = \frac{5}{5} + \frac{4}{5} = \frac{9}{5}$ .
Write with combined exponent: Write the expression with the combined exponent. $\newline$ The expression now is $9^{\frac{9}{5}}$ .
Simplify the expression: Simplify the expression. $9$ is $3^2$ , so we can rewrite $9^{\frac{9}{5}}$ as $(3^2)^{\frac{9}{5}}$ .
Apply exponent property: Apply the property of exponents that states $(a^m)^n = a^{m*n}$ . $\newline$ Multiply the exponents: $2 \times (\frac{9}{5}) = \frac{18}{5}$ .
Write final expression: Write the final expression. $\newline$ The simplified form is $3^{\frac{18}{5}}$ .