Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression. Express answers with positive exponents.
(-33xy^-1/66x^0y^-3)2
To raise the quantity in parentheses to the indicated exponent, you need to apply the exponent to each term separately. Let's break down the given expression step by step:
Expression: (-33xy^-1/66x^0y^-3)2
Step 1: Simplify the expression inside parentheses.
The exponent 2 applies to every term within the parentheses, so we need to raise each term to the power of 2.
-33^2 * x^1 * y^-1^2 / 66^2 * x^0^2 * y^-3^2
Simplifying further:
Step 2: Apply the power laws.
When raising a power to another power, you multiply the exponents.
(-33)^2 * x^1 * y^(-1*2) / (66)^2 * x^(0*2) * y^(-3*2)
Simplifying further:
Step 3: Simplify the exponents.
33^2 * x^1 * y^-2 / 66^2 * x^0 * y^-6
Step 4: Simplify the numerical values.
1089 * x * y^-2 / 4356 * 1 * y^-6
Step 5: Simplify further.
1089xy^-2 / 4356y^-6
Step 6: Apply the power law of negative exponents.
When a term has a negative exponent, it can be rewritten by moving it to the denominator with a positive exponent.
1089x / 4356y^(-6 - (-2))
Simplifying further:
Step 7: Simplify exponents.
1089x / 4356y^-4
Step 8: Apply the power law of negative exponents.
1089x / 4356 * (1/y^4)
Step 9: Simplify further.
1089x / 4356y^4
So, the simplified expression is 1089x / 4356y^4.