Simplify. ((3^(6))/(y^(-5)))^(2)=?

Write and apply power rule: Write down the given expression and apply the power of a quotient rule. The power of a quotient rule states that (a/b)^n = a^n / b^n. So, ((3^(6))/(y^(-5)))^(2) becomes (3^(6))^2 / (y^(-5))^2.Apply power of power rule: Apply the power of a power rule. The power of a power rule states that (a^m)^n = a^(m*n). So, (3^(6))^2 becomes 3^(6*2) and (y^(-5))^2 becomes y^(-5*2).Perform exponent multiplication: Perform the multiplication of the exponents. For 3^(6*2), multiply 6 by 2 to get 12, so 3^(6*2) becomes 3^12. For y^(-5*2), multiply -5 by 2 to get -10, so y^(-5*2) becomes y^(-10).Write simplified expression: Write down the simplified expression with the new exponents. The expression now is 3^12 / y^(-10).Simplify negative exponent: Simplify the expression with negative exponent. A negative exponent means that the base is on the wrong side of the fraction line, so you flip it to the other side. Therefore, y^(-10) becomes 1/y^10.Write final expression: Write down the final simplified expression. The final expression is 3^12 / (1/y^10), which can be written as 3^12 * y^10.

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Simplify. $\left(\frac{3^6}{y^{-5}}\right)^2=?$

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Algebra 1

Multiplication with rational exponents

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Q. Simplify.

\left(\frac{3^6}{y^{-5}}\right)^2=?

Write and apply power rule: Write down the given expression and apply the power of a quotient rule. $\newline$ The power of a quotient rule states that $(a/b)^n = a^n / b^n$ . $\newline$ So, $((3^{6})/(y^{-5}))^{2}$ becomes $(3^{6})^2 / (y^{-5})^2$ .
Apply power of power rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^m)^n = a^{m*n}$ . $\newline$ So, $(3^{6})^2$ becomes $3^{6*2}$ and $(y^{-5})^2$ becomes $y^{-5*2}$ .
Perform exponent multiplication: Perform the multiplication of the exponents. $\newline$ For $3^{6\times2}$ , multiply $6$ by $2$ to get $12$ , so $3^{6\times2}$ becomes $3^{12}$ . $\newline$ For $y^{(-5\times2)}$ , multiply $-5$ by $2$ to get $-10$ , so $y^{(-5\times2)}$ becomes $6$ $1$ .
Write simplified expression: Write down the simplified expression with the new exponents. $\newline$ The expression now is $3^{12} / y^{-10}$ .
Simplify negative exponent: Simplify the expression with negative exponent. $\newline$ A negative exponent means that the base is on the wrong side of the fraction line, so you flip it to the other side. Therefore, $y^{-10}$ becomes $\frac{1}{y^{10}}$ .
Write final expression: Write down the final simplified expression. $\newline$ The final expression is $3^{12} / (1/y^{10})$ , which can be written as $3^{12} \times y^{10}$ .