(y^−5)^−2
To simplify the expression, we apply the negative exponent rule, which states that \( (x^m)^{-n} = x^{-mn} \). Thus, \((y^{-5})^{-2} = y^{(-5)(-2)}\).
Multiplying the exponents, we find that \((-5)(-2) = 10\). Therefore, \((y^{-5})^{-2} = y^{10}\).
So, \((y^{-5})^{-2}\) simplifies to \(y^{10}\).
To simplify the expression (y^−5)^−2:
1. Start by applying the negative exponent rule. The negative exponent rule states that any term raised to a negative exponent can be rewritten as its reciprocal raised to the positive exponent.
(y^−5)^−2 becomes 1 / (y^5)^2.
2. Next, simplify the expression inside the parentheses. When raising a power to another exponent, you multiply the exponents:
(y^5)^2 = y^(5 * 2) = y^10.
3. So, the expression becomes 1 / y^10.
Therefore, the simplified form of (y^−5)^−2 is 1/y^10.
To simplify the expression (y^−5)^−2, you need to apply the exponent rules.
First, let's rewrite the expression using a negative exponent rule. The negative exponent rule states that any term with a negative exponent can be moved to the opposite position in the fraction and changed to a positive exponent.
So, (y^−5)^−2 can be rewritten as 1 / (y^5)^2.
Next, when you raise a power to another power, you need to multiply the exponents. In this case, we have (y^5)^2, and when we apply the exponent rule, we multiply the exponents 5 and 2 to get a final exponent of 10.
So, the expression becomes 1 / y^10.
Therefore, the simplified form of (y^−5)^−2 is 1 / y^10.