A ratio of 4:1 means that there are 4 home fans for every one visiting fan. So, of every 5 fans, 4 are home fans and \( \frac{4}{5} \) of every fan in the stadium is a home fan:

48,000 fans x \( \frac{4}{5} \) = \( \frac{192000}{5} \) = 38,400 fans.

To multiply terms with exponents, the base of both exponents must be the same. In this case they are so multiply the coefficients and add the exponents:

-2c⁶ x 3c²
(-2 x 3)c^{(6 + 2)}
-6c⁸

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

If 68% of the town's 29,000 voters cast ballots the number of votes cast is:

(\( \frac{68}{100} \)) x 29,000 = \( \frac{1,972,000}{100} \) = 19,720

The mayor got 75% of the votes cast which is:

(\( \frac{75}{100} \)) x 19,720 = \( \frac{1,479,000}{100} \) = 14,790 votes.

A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

0.0001315 in scientific notation is 1.315 x 10^-4