The expression (4𝑥13𝑦−1)32(𝑥𝑦)52 can be written in the form 𝑝×𝑥𝑞×𝑦𝑟, where 𝑝,𝑞,𝑟 are integers. What is 𝑝+𝑞+𝑟 ? (Give only the number as your answer.)

Question

The expression (4𝑥13𝑦−1)32(𝑥𝑦)52 can be written in the form 𝑝×𝑥𝑞×𝑦𝑟, where 𝑝,𝑞,𝑟 are integers. What is 𝑝+𝑞+𝑟 ? (Give only the number as your answer.)

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Solution

First, let's simplify the expression:

(4𝑥^13𝑦^−1)^32(𝑥𝑦)^52

= 4^32 * x^(1332) * y^(-132) * x^52 * y^52

= 4^32 * x^(416+52) * y^(52-32)

= 4^32 * x^468 * y^20

So, 𝑝=4^32, 𝑞=468, 𝑟=20.

Then, 𝑝+𝑞+𝑟 = 4^32 + 468 + 20 = 4294967700.

Similar Questions

𝑆𝑢𝑝𝑝𝑜𝑠𝑒 𝑡ℎ𝑎𝑡 𝑡ℎ𝑒 𝑐ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐 𝑝𝑜𝑙𝑦𝑛𝑜𝑚𝑖𝑎𝑙 𝑜𝑓 𝑠𝑜𝑚𝑒 𝑚𝑎𝑡𝑟𝑖𝑥 𝐴 𝑖𝑠 𝑓𝑜𝑢𝑛𝑑 𝑡𝑜 𝑏𝑒 𝑝(𝜆) = (𝜆 - 1)𝜆 -32 𝜆 -43 . 𝑊ℎ𝑎𝑡 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑖𝑧𝑒 𝑜𝑓 𝐴?

Select the correct answer.Which expression is equivalent to 5⁢log𝑥⁡2−log𝑥⁡4? A. log𝑥⁡6 B. log𝑥⁡(52) C. log𝑥⁡28 D. log𝑥⁡8

Solve 3𝑥 + 13𝑦 ≡ 8(𝑚𝑜𝑑 55), 5𝑥 + 21𝑦 ≡ 34(𝑚𝑜𝑑 55)

What is the rule for this pattern?32,36,40,44

Using exponential notation, we can write 32 as

1/1

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