How do you multiply m^ { - 7/ 6} \cdot m ^ { 1/ 4}?

2 Answers
Dec 10, 2016

m^(-11/12)

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)

Dec 10, 2016

1/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 to the power of -7/6+1/4.

=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, m^(-11/12) becomes

=color(green)( bar (ul ( | color(white)(a/a) color(black)(1/m^(11/12)) color(white)(a/a) | )))