(y^-5)^-10y^10
(y^-5)^-10 y^10 = y^(-5 * -10) y^10 = y^50 y^10 = y^60
Well, well, well, looks like we have a little math problem here. Let's see if we can solve it!
First, let's simplify the expression inside the parentheses. When you raise something to a negative power, it flips the base and puts it in the denominator. So, (y^-5) becomes 1/y^5.
Now we have (1/y^5)^-10y^10.
To simplify this, we can use the power of a power rule. When you raise an exponent to another exponent, you multiply the exponents. So, (-10) * (y^10) gives us -10y^10.
Now, we have (1/y^5)^-10y^10, which simplifies to 1/(y^5 * -10y^10).
Finally, we can simplify this further by combining the y exponents. When you multiply with the same base, you add the exponents. So, y^5 * y^10 becomes y^15.
In the end, we have 1/(y^15 * -10y^10).
And that, my friend, is one complicated expression. I hope my clown antics helped you understand it a bit better!
To simplify the expression, let's break it down step-by-step:
Step 1: Simplify the exponent inside the parentheses.
(y^(-5))^(-10y^10)
The exponent inside the parentheses is -5, so we can rewrite the expression as:
1/(y^5)^(-10y^10)
Step 2: Apply the power of a power rule.
1/(y^5)^(-10y^10)
= 1/y^(-50y^10)
Step 3: Apply the power of a power rule again.
1/y^(-50y^10)
= y^(50y^10)
Therefore, the simplified expression is y^(50y^10).
To simplify the expression (y^-5)^-10y^10, we can use the rule of exponentiation that states (a^m)^n = a^(m * n). Let's break down the expression step by step:
Step 1: Simplify the inner exponent.
In this case, the inner exponent of (y^-5)^-10 is -10 * y^-5. Using the power of a power rule, we multiply the exponents to get -10 * -5 = 50. Therefore, the expression becomes y^50.
Step 2: Simplify the outer exponent.
Now we have y^50 * y^10. When multiplying variables with the same base, we add their exponents. Hence, y^50 * y^10 = y^(50 + 10) = y^60.
Therefore, the simplified form of (y^-5)^-10y^10 is y^60.