Question

find the product of. X × X² × X³ × X⁴​

Answer 1

Answer:

Step-by-step explanation:

= X ^(1+2+3+4)

= X ^10

Answer 2

Answer:

Required product is ${x}^{10}$

Step-by-step explanation:

Given,

$x \times {x}^{2} \times {x}^{3} \times {x}^{4}$

We want to find value of the given term.

We know,

${a}^{b} \times {a}^{c} = {a}^{b + c}$

For example,

${2}^{3} \times {2}^{5} = {2}^{3 + 5} \\ = {2}^{8}$

and

${3}^{10} \times {3}^{20} \\ = {3}^{10 + 20} \\ = {3}^{30}$

Now,

$x \times {x}^{2} \times {x}^{3} \times {x}^{4} \\ = {x}^{1 + 2} \times {x}^{3 + 4} \\ = {x}^{3} \times {x}^{7} \\ = {x}^{3 + 7} \\ = {x}^{10}$

This is a problem of Power of indices.

Some important formulas of Power of indices :

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

#SPJ2