The expression ((m^(2))/(m^((1)/(3))))^(-(1)/(2)) is equivalent to (1) root(16)(m^(5)) (3) -mroot(5)(m) (2) (1)/(root(6)(m^(5))) (4) (1)/(mroot(3)(m))

Simplify inside parentheses: We start by simplifying the expression inside the parentheses before dealing with the outer negative exponent. The expression inside the parentheses is a quotient of powers with the same base, so we can subtract the exponents. (m^(2))/(m^((1)/(3))) = m^(2 - 1/3) = m^(6/3 - 1/3) = m^(5/3)Apply negative exponent: Now we apply the outer exponent of -1/2 to the simplified base. (m^(5/3))^(-(1)/(2)) = m^((5/3) * -(1/2)) = m^(-5/6)Reciprocal of base: The negative exponent indicates that the expression is the reciprocal of the base with the positive exponent. m^(-5/6) = 1/(m^(5/6))Rewrite as radical expression: The expression 1/(m^(5/6)) can be rewritten as a radical expression. 1/(m^(5/6)) = (1)/(root(6)(m^(5)))Compare with options: We compare the simplified expression with the given options. The correct option that matches our simplified expression is option (2) (1)/(root(6)(m^(5))).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The expression
((m^(2))/(m^((1)/(3))))^(-(1)/(2)) is equivalent to
(1)
root(16)(m^(5))
(3)
-mroot(5)(m)
(2)
(1)/(root(6)(m^(5)))
(4)
(1)/(mroot(3)(m))

The expression $\left(\frac{m^{2}}{m^{\frac{1}{3}}}\right)^{-\frac{1}{2}}$ is equivalent to $\newline$ ( $1$ ) $\sqrt[16]{m^{5}}$ $\newline$ ( $3$ ) $-m \sqrt[5]{m}$ $\newline$ ( $2$ ) $\frac{1}{\sqrt[6]{m^{5}}}$ $\newline$ ( $4$ ) $\frac{1}{m \sqrt[3]{m}}$

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. The expression

\left(\frac{m^{2}}{m^{\frac{1}{3}}}\right)^{-\frac{1}{2}}

is equivalent to

\newline

(

1

)

\sqrt[16]{m^{5}}

\newline

(

3

)

-m \sqrt[5]{m}

\newline

(

2

)

\frac{1}{\sqrt[6]{m^{5}}}

\newline

(

4

)

\frac{1}{m \sqrt[3]{m}}

Simplify inside parentheses: We start by simplifying the expression inside the parentheses before dealing with the outer negative exponent. $\newline$ The expression inside the parentheses is a quotient of powers with the same base, so we can subtract the exponents. $\newline$ $\frac{m^{2}}{m^{\frac{1}{3}}} = m^{2 - \frac{1}{3}} = m^{\frac{6}{3} - \frac{1}{3}} = m^{\frac{5}{3}}$
Apply negative exponent: Now we apply the outer exponent of $-\frac{1}{2}$ to the simplified base. $\newline$ $(m^{\frac{5}{3}})^{-\frac{1}{2}} = m^{(\frac{5}{3} \cdot -\frac{1}{2})} = m^{-\frac{5}{6}}$
Reciprocal of base: The negative exponent indicates that the expression is the reciprocal of the base with the positive exponent. $m^{-\frac{5}{6}} = \frac{1}{m^{\frac{5}{6}}}$
Rewrite as radical expression: The expression $\frac{1}{m^{\frac{5}{6}}}$ can be rewritten as a radical expression. $\newline$ $\frac{1}{m^{\frac{5}{6}}} = \frac{1}{\sqrt[6]{m^{5}}}$
Compare with options: We compare the simplified expression with the given options. $\newline$ The correct option that matches our simplified expression is option $(2)$ $\left(\frac{1}{\sqrt[6]{m^{5}}}\right)$ .