Solve (6²)¹³: Calculating a Power of Power Expression

When you have $(6^2)^{13}$, you're taking $6^2$ and using it as a base 13 times. This means $6^2 \times 6^2 \times ... \times 6^2$ (13 times), which equals $6^{2+2+...+2} = 6^{26}$.

Great question! $6^2 \times 6^{13} = 6^{2+13} = 6^{15}$ uses the product rule (add exponents). But $(6^2)^{13} = 6^{2 \times 13} = 6^{26}$ uses the power rule (multiply exponents).

You'd get $36^{13}$, which is correct but much harder to work with! It's better to use the power rule: $(6^2)^{13} = 6^{26}$ keeps everything in simplest exponential form.

Parentheses = Multiply: $(a^n)^m = a^{n \times m}$
Same base multiplication = Add: $a^n \times a^m = a^{n+m}$
Look for those parentheses around the base!

Yes! The power rule $(a^n)^m = a^{n \times m}$ works with any base and any exponents - positive, negative, fractions, or even variables like $(x^3)^4 = x^{12}$.