The value of p from the given indices expression is 43.
Applying the law of indices as shown:
[tex](a^m)^n = a^{mn}[/tex] where a, m and n are integers
Given the indices expression:
[tex](x^{22})(x^7)^3[/tex]
This can also be expressed as:
[tex]x^{22} \times x^{7\times 3}\\x^{22} \times x^{21[/tex]
Since [tex]a^m * a^n = a^{m+n}[/tex]
[tex]x^{22} \times x^{21} = x^{22+21}=x^{43[/tex]
Comparing [tex]x^{43} \ with \ x^p[/tex]
[tex]x^{43}=x^p\\Equating \ the \ powers\\43 = p\\p=43[/tex]
Hence the value of p from the given indices expression is 43.
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