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Ludmilka [50]
3 years ago
9

Which expression is equivalent to 1/27 ( 1 over 27 ) ?

Mathematics
2 answers:
kicyunya [14]3 years ago
4 0

The expression equivalent to \frac{1}{{27}}is\boxed{{\mathbf{Option D}}-{{\mathbf{3}}^{\mathbf{4}}}{\mathbf{ \times }}{{\mathbf{3}}^{{\mathbf{-7}}}}}.

Further explanation:

The expression is given as\frac{1}{{27}}.

Now, the above expression is simplified as follows:

\begin{aligned}\frac{1}{{27}}&=\frac{1}{{3 \times 3 \times 3}}\\&=\frac{1}{{{3^3}}}\\\end{aligned}

Now, the power rule for rational exponent is given below.

The expression {a^{ - n}} equivalent to expression \frac{1}{{{a^n}}} that is\boxed{\frac{{\mathbf{1}}}{{\mathbf{a}}}{\mathbf{ = }}{{\mathbf{a}}^{{\mathbf{ - n}}}}}.

In the expression\frac{1}{{{3^3}}}, the value of a = 3andn = 3.

The simplified form of the expression \frac{1}{{{3^3}}} as follows:

\begin{aligned}\frac{1}{{{3^3}}}&={3^{-3}}\\&={3^{\left({-7+4}\right)}}\\\end{aligned}

From the exponent rule\boxed{{{\mathbf{a}}^{{\mathbf{m + n}}}}{\mathbf{ = }}{{\mathbf{a}}^{\mathbf{m}}}{\mathbf{ \times }}{{\mathbf{a}}^{\mathbf{n}}}}, the above expression is evaluated as follows:

\begin{aligned}\frac{1}{{27}}&={3^{\left({-7+4}\right)}}\\&={3^{\left({ - 7} \right)}}\cdot {3^4}\\\end{aligned}

Therefore, the expression equivalent to \frac{1}{{27}}is\boxed{{{\mathbf{3}}^{\mathbf{4}}}{\mathbf{ \times }}{{\mathbf{3}}^{{\mathbf{ - 7}}}}}.

Now, the four options are given below.

\begin{aligned}&{\text{OPTION A}}\to{{\text{3}}^1}\times {3^{ - 10}}\hfill\\&{\text{OPTION B}}\to{{\text{3}}^{-1}}\times {3^{10}}\hfill\\&{\text{OPTION C}}\to{{\text{3}}^{-4}}\times {3^7}\hfill\\&{\text{OPTION D}}\to{{\text{3}}^4}\times{3^{-7}}\hfill\\\end{aligned}

Here, OPTION A is{{\text{3}}^1} \times {3^{ - 10}}.

The simplified form of OPTION A {{\text{3}}^1} \times {3^{ - 10}} is given below.

\begin{aligned}{{\text{3}}^1}\times{3^{-10}}&={3^{1+\left({-10}\right)}}\\&={3^{1-10}}\\&={3^{-9}}\\\end{aliged}

The above solution {3^{-9}} of the expression {{\text{3}}^1}\times{3^{-10}}does not matches with the obtained solution{3^4}\times{3^{-7}}.

The simplified form of OPTION B {{\text{3}}^{-1}}\times{3^{10}} is given below.

\begin{aligned}{{\text{3}}^{-1}}\times{3^{10}}&={3^{-1+10}}\\&={3^9}\\\end{aligned}

The above solution {3^9} of the expression {{\text{3}}^{-1}}\times{3^{10}}does not matches with the obtained solution{3^4}\times{3^{-7}}.

The simplified form of OPTION C {{\text{3}}^{-4}}\times{3^7} is given below.

\begin{aligned}{{\text{3}}^{-4}}\times{3^7}&={3^{-4+7}}\\&={3^3}\\\end{aligned}

The above solution {3^3} of the expression {{\text{3}}^{-4}}\times{3^7}does not matches with the obtained solution{3^4}\times{3^{-7}}.

OPTION D is given as {3^4}\times{3^{-7}}and it matches with the obtained solution{3^4}\times{3^{-7}}.

From above four options, the expression equivalent to \frac{1}{{27}}is{{\mathbf{3}}^{\mathbf{4}}}{\mathbf{ \times }}{{\mathbf{3}}^{{\mathbf{ - 7}}}}.

Thus, the expression equivalent to \frac{1}{{27}}is\boxed{{\mathbf{Option D}} - {{\mathbf{3}}^{\mathbf{4}}}{\mathbf{ \times }}{{\mathbf{3}}^{{\mathbf{ - 7}}}}}.

Learn more:

1. Which expression is equivalent to ?brainly.com/question/3658196

2. What are the values of x?brainly.com/question/2093003

3. Which expression is a sum of cubes?brainly.com/question/4102355

Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Exponents and expressions

Keywords:expression, exponent, power exponent, equivalent, match, options,{3^4} \times {3^{ - 7}},\frac{1}{{27}}

harkovskaia [24]3 years ago
3 0

Answer:

Option D

Step-by-step explanation:

Option A:

(3)¹ × (3)⁻¹⁰   =  (3)⁽¹⁻¹⁰⁾   = 3⁹

= 4\frac{1}{3^9}

= 4\frac{1}{19683}

Option B :

(3)⁻¹ × (3) ¹⁰   = 3⁽¹⁰⁻¹⁾

= 3⁹

= 19683

Option C :

(3⁻⁴) × (3)⁷   = 3⁽⁷⁻⁴⁾

               = 3³

Option D :

3⁴ × 3⁻⁷ = 3⁴⁻⁷

= 3⁻³

=  4\frac{1}{3^3}

= 4\frac{1}{27}

Therefore, option D is the answer.

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