how do you expand completely:
(x to the fourth power y to the fifth)entire problem to the fifth.
do you just add the exponents?
(answer x to the 9th - y to the 6th)
when you raise to powers, you multiply exponents. Consider:
2^3 = 2*2*2
(2^3)^4 = (2*2*2)*(2*2*2)*(2*2*2)*(2*2*2) = 2^(3+3+3+3) 2^(3*4) = 2^12
So,
(x^4 y^5)^5 = x^20 y^25
(x^4 y^5)^5
= (x^4)^5 (y^5)^5
= x^20 y^25
To expand the expression (x^4y^5) to the fifth power, you can apply the rule of exponents, which states that when you raise a power to another power, you need to multiply the exponents.
So, to raise (x^4y^5) to the fifth power, you need to multiply the exponents of x and y by 5. Here's the step-by-step process:
1. Apply the exponent to each base individually: (x^4)^5 * (y^5)^5.
2. Multiply the exponents by 5: x^(4*5) * y^(5*5).
3. Simplify the exponents: x^20 * y^25.
Therefore, the expanded expression of (x^4y^5) to the fifth power is x^20 * y^25.