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Len [333]
2 years ago
14

Please solve this thank you!

Mathematics
2 answers:
SSSSS [86.1K]2 years ago
6 0

Answer:

1024x^{40}

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:

[\frac{8x^9}{2x}]^5

Divide by 2x (divide coefficient by 2, subtract coefficient degrees)

[4x^8]^5

Multiply exponents and raise 4 to the power of 5

1024x^{40}

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

Tamiku [17]2 years ago
4 0

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

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