Question

Use the laws of exponents to simplify.
6^(3/4)*6^(5/8)

Answer 1

hint: when multiplying exponential expressions with the same base, you add the exponents to get a simplified answer.

Answer 2

make for exponent 3/4 + 5/8

Answer 3

Think about a simple example...

\[X ^{2} =X*X\]
\[X ^{3}=X*X*X\]
\[X ^{2}*X ^{3} = (X*X)(X*X*X)\]
\[X ^{2}*X ^{3} = X*X*X*X*X\]
\[X ^{2}*X ^{3} = X^{5}\]

All you have to do is add the exponents together.

\[X^{m}*X^{n}= X^{m+n}\]

get the exponents to have the same denominator. Turn 3/4 into 6/8.

\[6^{3/4}*6^{5/8}= 6^{6/8}*6^{5/8}\]

Then add the exponents together.

\[6^{6/8}*6^{5/8}=6^{11/8}\]