How do you multiply m^ { - 7/ 6} \cdot m ^ { 1/ 4}?
2 Answers
Explanation:
Using the
color(blue)"law of exponents"
color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(a^mxxa^n=a^(m+n))color(white)(2/2)|)))
rArrm^(-7/6)xxm^(1/4)=m^(-7/6+1/4)
"Now " -7/6+1/4=-28/24+6/24=-22/24=-11/12
rArrm^(-7/6+1/4)=m^(-11/12)
Explanation:
Recall the product rule for exponents:
color(blue)(bar(ul(|color(white)(a/a)a^m*a^n=a^(m+n)color(white)(a/a)|))) When you are multiplying two powers with the same base, you add their exponent values together.
Applying the rule to the given question,
m^(-7/6)*m^(1/4)
The expression becomes
=m^(-7/6+1/4)
Since the fractions being added together do not have a common denominator, rewrite each fraction so that each one has the same denominator.
=m^(-14/12+3/12)
Evaluating,
=m^(-11/12) However, expressions with negative exponents are usually simplified so that it only contains positive exponents.
Recall the negative exponent rule:
color(blue)(bar(ul(|color(white)(a/a)a^-m=1/a^mcolor(white)(a/a)|)))
Hence,
=color(green)( bar (ul ( | color(white)(a/a) color(black)(1/m^(11/12)) color(white)(a/a) | )))