Input a set of exponential expressions to quickly calculate their product.
If the bases are the same, add the exponents while keeping the base unchanged. The formula is: \( a^m \times a^n = a^{m+n} \)
Solution:
\( 4^2 \times 4^3 = 4^{2 + 3} = 4^5 = 1024 \)
So, \( 4^2 \times 4^3 = 1024 \)
If the bases are different, calculate each exponent separately, then multiply the results.
For example: a^m, b^n, c^p
2^4; 3^3; 5^1
a^m, b^n, c^p; 2^4; 3^3; 5^1
Solution:
Input (comma separated): 2^4, 2^3
Same base, add exponents:
\( 2^4 \times 2^3 = 2^{4 + 3} = 2^7 = 128 \)
Result: \( 2^4 \times 2^3 = 128 \)
Solution:
Input (semicolon separated): 5^2; 7^3; 3^4
Calculation:
\( 5^2 = 25 \)
\( 7^3 = 343 \)
\( 3^4 = 81 \)
\( 25 \times 343 \times 81 = 694575 \)
Result: \( 5^2 \times 7^3 \times 3^4 = 694575 \).
Solution:
Input (comma and semicolon separated): 10^2, 2^5; 3^3
Calculation:
\( 10^2 = 100 \)
\( 2^5 = 32 \)
\( 3^3 = 27 \)
\( 100 \times 32 \times 27 = 86400 \)
Result: \( 10^2 \times 2^5 \times 3^3 = 86400 \).