How to write the following as a single power of 5

Question

(25^6 *5^8) / 625^4

Answer 1

Note that fractions = Numerator/Denominator

Numerator calculations:

1. We can re-write the numerator as = (25^6 *5^8) = ((5^2)^6) * 5^8) so that everything has a base of 5.

Note: a power to the power rule means that we would multiply the two exponents together.

1. The numerator is therefore = (5^12)*(5^8).

Note: When you are multiplying two exponents of the same base, add the exponents

1. The numerator is now = 5^20

Denominator calculations:

1. We can re-write 625^4 as (5^4)^4

Note: Again, we see here a power to the power. So we would multiply the exponents.

1. The denominator is therefore = 5^16

Put Numerator and Denominator together = 5^20/5^16

Note: Exponents in division we would subtract the two.

Final answer is = 5^4