(16^(5//9)*5^(7//9))^(-3)

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Identify Equation & Apply Property: Identify the equation and apply the power of a product property. The power of a product property states that (ab)^c = a^c * b^c. We will apply this property to the given expression. (16^(5/9) * 5^(7/9))^(-3) = 16^((5/9)*(-3)) * 5^((7/9)*(-3))Simplify Exponents by Multiplying: Simplify the exponents by multiplying them. We need to multiply the exponents by -3. 16^((5/9)*(-3)) = 16^(-5/3) 5^((7/9)*(-3)) = 5^(-7/3)Write 16 as Power of 2: Write 16 as a power of 2. 16 is 2 raised to the 4th power, so we can rewrite 16^(-5/3) as (2^4)^(-5/3). (2^4)^(-5/3) = 2^(4*(-5/3)) = 2^(-20/3)Simplify Expression 2^(-20/3): Simplify the expression 2^(-20/3). The negative exponent indicates the reciprocal, so 2^(-20/3) is the same as 1/(2^(20/3)). 1/(2^(20/3))Simplify Expression 5^(-7/3): Simplify the expression 5^(-7/3). Similarly, the negative exponent indicates the reciprocal for 5^(-7/3), so it becomes 1/(5^(7/3)). 1/(5^(7/3))Combine Reciprocal Expressions: Combine the two reciprocal expressions. Now we combine the expressions from Step 4 and Step 5. 1/(2^(20/3)) * 1/(5^(7/3)) = 1/(2^(20/3) * 5^(7/3))Simplify Combined Expression: Simplify the combined expression. Since we are multiplying the denominators, we can combine them under a single denominator. 1/(2^(20/3) * 5^(7/3)) = 1/(2^20 * 5^7)^(1/3)Recognize Math Error: Recognize a math error in the previous step. The exponents should not be multiplied together when combining the denominators. This is a math error.

$(16^{\frac{5}{9}} \cdot 5^{\frac{7}{9}})^{-3}$

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$(16^{\frac{5}{9}} \cdot 5^{\frac{7}{9}})^{-3}$