Perform the indicated operation and simplify each expression (x132y−14)(6x124y23)

Consider the provided expression, (x132y−14)(6x124y23) Simplify the provided expression, Remove the provided brackets we get, x132y−14⋅6x124y23 Multiply by the given expression, ab⋅cd=a⋅cb⋅d We get, x132y−14⋅6x124y23 Apply the exponent rule 1xb⋅xa=1xb+a x132y−14⋅6x124y23=6x568y512 =3x564y512 Hence. Consider the provided expression, 3{−27x12yz5} Express the given radical expression in the exponential form, Apply the radical rule n{−a}=−n{a} if n is odd. 3{−27x12yz5}=−3{27x12yz5} Apply the radical rule n{abc}=n{a}n{b}n{c}:a≥0,b≥0,c≥0 We get, 3{−27x12yz5}=−3{(3)3x12yz5}

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Algebra I
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Globokim8

Answered question

2021-09-10

Perform the indicated operation and simplify each expression

(\frac{x^{\frac{1}{3}}}{2 y^{- \frac{1}{4}}}) (\frac{6 x^{\frac{1}{2}}}{4 y^{\frac{2}{3}}})

Answer & Explanation

dessinemoie

Skilled2021-09-11Added 90 answers

Consider the provided expression,

(\frac{x^{\frac{1}{3}}}{2 y^{- \frac{1}{4}}}) (\frac{6 x^{\frac{1}{2}}}{4 y^{\frac{2}{3}}})

Simplify the provided expression,
Remove the provided brackets we get,

\frac{x^{\frac{1}{3}}}{2 y^{- \frac{1}{4}}} \cdot \frac{6 x^{\frac{1}{2}}}{4 y^{\frac{2}{3}}}

Multiply by the given expression,

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

We get,

\frac{x^{\frac{1}{3}}}{2 y^{- \frac{1}{4}}} \cdot \frac{6 x^{\frac{1}{2}}}{4 y^{\frac{2}{3}}}

Apply the exponent rule

\frac{1}{x^{b} \cdot x^{a}} = \frac{1}{x^{b + a}}

\frac{x^{\frac{1}{3}}}{2 y^{- \frac{1}{4}}} \cdot \frac{6 x^{\frac{1}{2}}}{4 y^{\frac{2}{3}}} = \frac{6 x^{\frac{5}{6}}}{8 y^{\frac{5}{12}}}

= \frac{3 x^{\frac{5}{6}}}{4 y^{\frac{5}{12}}}

Hence.
Consider the provided expression,

\sqrt{3} {- 27 x^{12} y z^{5}}

Express the given radical expression in the exponential form,
Apply the radical rule

\sqrt{n} {- a} = - \sqrt{n} {a}

if n is odd.

\sqrt{3} {- 27 x^{12} y z^{5}} = - \sqrt{3} {27 x^{12} y z^{5}}

Apply the radical rule

\sqrt{n} {a b c} = \sqrt{n} {a} \sqrt{n} {b} \sqrt{n} {c} : a \geq 0, b \geq 0, c \geq 0

We get,

\sqrt{3} {- 27 x^{12} y z^{5}} = - \sqrt{3} {{(3)}^{3} x^{12} y z^{5}}

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