Answer :
Using the Product, Quotient, Power rule of exponents, the simplified result of ((-45x⁹y⁵) / (9x⁴y²))⁰ is 1.
Let's simplify the expression using the product, quotient, and power rules of exponents,
Product rule is aᵇ. aⁿ = a ᵇ⁺ⁿ
Quotient Rule is aᵇ / aⁿ = aᵇ⁻ⁿ
Power Rule is a⁰ = 1
The given expression is, ((-45x⁹y⁵) / (9x⁴y²))⁰
First, the quotient rule of exponents by subtracting the exponent in the denominator from the exponent in the numerator for both x and y terms:
Now the expression becomes, (-5x³y³)⁰
By applying the power rule,
(-5x³y³)⁰ = 1
So, the simplified result of ((-45x⁹y⁵) / (9x⁴y²))⁰ is 1.
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The value of the given expression raised to the power of 0 is 1.
To solve the expression[tex]((-45x^(9)y^(5))/(9x^(4)y^(2)))^0[/tex] using the product, quotient, and power rules of exponents, we can break down the given expression step by step.
First, we apply the quotient rule of exponents by subtracting the exponent in the denominator from the exponent in the numerator for both x and y terms:
[tex]((-45x^(9)y^(5))/(9x^(4)y^(2))) = -5x^(9-4)y^(5-2) = -5x^5y^3[/tex]
Now, we have the expression [tex]-5x^5y^3[/tex]. To apply the power rule, any non-zero number raised to the power of 0 is equal to 1:
[tex](-5x^5y^3)^0 = 1[/tex]
Therefore, the result of the expression [tex]((-45x^(9)y^(5))/(9x^(4)y^(2)))^0[/tex] is 1.
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