ANSWER:
The product of given two terms [tex]\left(x^{2}\right)^{3} \text { and } x^{4} \text { is } x^{10}[/tex]
SOLUTION:
Given, two terms are [tex]\left(x^{2}\right)^{3} \text { and } x^{4}[/tex]
First term is in indirect form, so let us convert it into direct form first.
we know the identity [tex]\left(a^{m}\right)^{n}=a^{m \times n}[/tex]
applying this identity in above expression, [tex]\left(x^{2}\right)^{3}=x^{2 \times 3}[/tex]becomes,
[tex]\left(x^{2}\right)^{3}=x^{6}[/tex]
As the the second term is in direct form, we can now multiply both the terms.
Now, product of two terms = [tex]x^{6} \times x^{4}[/tex]
we know the identity [tex]a^{m} \times a^{n}=a^{m+n}[/tex]
when exponential terms with same base are multiplied, power should be added. So we get [tex]X^{6+4}[/tex]
[tex]X^{6+4}=X^{10}[/tex]
Hence the product of two terms [tex]\left(x^{2}\right)^{3} \text { and } x^{4} \text { is } x^{10}[/tex]
