Answer:
[tex]1024x^{40}[/tex]
Step-by-step explanation:
So the first step is to add like terms since you can simplify the numerator by adding the two values sine they have the same variable and degree.
Add like terms:
[tex][\frac{8x^9}{2x}]^5[/tex]
Divide by 2x (divide coefficient by 2, subtract coefficient degrees)
[tex][4x^8]^5[/tex]
Multiply exponents and raise 4 to the power of 5
[tex]1024x^{40}[/tex]
The reason you multiply exponents is because you can think about it like this:
(4 * x * x * x * x * x * x * x * x) (this has one 4 and 8 x's because x is raised to the power of 8. Now if you do that 5 times which is what the exponent is doing you're going to have 40 x's and 8 4's. So it's essentially
(4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x) * (4 * x * x * x * x * x * x * x * x). If you group like terms you'll get (4 * 4 * 4 * 4 * 4) * (x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x * x). Which simplifies to 4^5 * x ^ (8 * 5) which further simplifies to the answer 1024x^40
Answer:
1024x^40
Step-by-step explanation:
Apply exponent rule: (a/b)^c = a^c / b^c = (5x^9 + 3x^9)^5 / (2x)^5
Simplify:
(5x^9 + 3x^9)^5: 32768x^45
= 32768x^45 / (2x)^5
Simplify:
(2x)^5: 32x^5
= 32768x^45 / 32x^5
Divide the numbers: 32768 / 32 = 1024
= 1024x^45 / x^5
Apply exponent rule: x^a / x^b = x^a - b
x^45 / x^5 = x^45 - 5
= 1024x^45 - 5
Subtract the numbers: 45 - 5 = 40
= 1024x^40
