Answer:
[tex]a^2 \cdot \left(a^4\right)^3 \div a^{13}=a[/tex]
Step-by-step explanation:
Given expression:
[tex]a^2 \cdot \left(a^4\right)^3 \div a^{13}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies a^2 \cdot a^{(4 \cdot 3)} \div a^{13}[/tex]
[tex]\implies a^2 \cdot a^{12} \div a^{13}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies a^{(2+12)} \div a^{13}[/tex]
[tex]\implies a^{14} \div a^{13}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \div a^c=a^{b-c}:[/tex]
[tex]\implies a^{(14-13)}[/tex]
[tex]\implies a^1[/tex]
[tex]\textsf{Apply exponent rule} \quad a^1=a:[/tex]
[tex]\implies a[/tex]
Learn more about exponent rules here:
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