Question

express the following product as a monomial (a50 b51)(b49 c67) (c33d) (d100a100)​

Answer 1

Answer:

(ab101) ,(bc116) ,(cd33) , (da200)

Answer 2

Correct question is "Express the following product as a monomial (a⁵⁰ b⁵¹)(b⁴⁹c⁶⁷) (c³³d) (d¹⁰⁰a¹⁰⁰)".

Answer:

Required polynomial is $a^{150} b^{100} c^{100} d^{101}.$

Step-by-step explanation:

Given expression is (a⁵⁰ b⁵¹)(b⁴⁹c⁶⁷) (c³³d) (d¹⁰⁰a¹⁰⁰)

To express the given product as a monomial, we need to multiply all the powers of each variable together.

Starting with "a", we have:

$a^{50} \times a^{100 }= a^{50+100}= a^{150}$

Moving on to "b":

$b^{51} \times b^{49} = b^{(51+49)} = b^{100}$

And for "c":

$c^{67} \times c^{33} = c^{(67+33)} = c^{100}$

Finally, for "d":

$d^1 \times d^{100} = d^{(1+100)} = d^{101}$

Now, we can combine all the terms:

$a^{150} \times b^{100} \times c^{100} \times d^{101}$

Therefore, the given product expressed as a monomial is

$a^{150} b^{100} c^{100} d^{101}.$

This is a problem of power of indices.

Some important formulas of Power of indices ,

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$

Know more about Power of indices,

1.https://brainly.in/question/21620304

2.https://brainly.in/question/10752814

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