Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$Express the following fraction in simplest form using only positive exponents. (6a^(5))/(3(a^(2))^(5)) Answer:$

Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{6 a^{5}}{3\left(a^{2}\right)^{5}}$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Multiplication with rational exponents

Full solution

Q. Express the following fraction in simplest form using only positive exponents.

\newline

\frac{6 a^{5}}{3\left(a^{2}\right)^{5}}

\newline

Answer:

Identify Factors: Write down the given expression and identify the common factors in the numerator and the denominator. $\newline$ The given expression is $(6a^{5})/(3(a^{2})^{5})$ . $\newline$ We can see that both the numerator and the denominator have common factors of $a$ and numerical coefficients that can be simplified.
Simplify Coefficients: Simplify the numerical coefficients. $\newline$ The numerical coefficient in the numerator is $6$ and in the denominator is $3$ . We can divide $6$ by $3$ to simplify this part of the expression. $\newline$ $6 \div 3 = 2$ $\newline$ So, the expression now is $2a^{5}/(a^{2})^{5}$ .
Simplify Exponents: Simplify the exponential terms. $\newline$ We have $a^{5}$ in the numerator and $(a^{2})^{5}$ in the denominator. According to the power of a power rule, $(a^{2})^{5}$ is equal to $a^{2*5}$ or $a^{10}$ . $\newline$ So, the expression now is $\frac{2a^{5}}{a^{10}}$ .
Apply Quotient Rule: Apply the quotient rule for exponents. $\newline$ The quotient rule states that when dividing like bases, you subtract the exponents. So, $a^{5}/a^{10}$ is $a^{5-10}$ or $a^{-5}$ . $\newline$ The expression now is $2a^{-5}$ .
Rewrite with Positive Exponents: Rewrite the expression with only positive exponents. $\newline$ Since we want only positive exponents, we can write $a^{-5}$ as $\frac{1}{a^{5}}$ . $\newline$ The final simplified expression is $\frac{2}{a^{5}}$ .

More problems from Multiplication with rational exponents

Question

\newline

81^{\frac{1}{2}}

\newline

Posted 9 months ago

Question

\newline

(-32)^{1/5}

\newline

Posted 9 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{4}{3}}}{w^{\frac{7}{3}}}

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 5 months ago

Question

Simplify. Assume all variables are positive.

\newline

(2r^{\frac{1}{3}})^8

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 5 months ago

Question

Simplify. Assume all variables are positive.

\newline

v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 5 months ago

Question

\newline

1^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}

\newline

Posted 5 months ago

Question

\newline

32^{(-1/5)}

Posted 7 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 9 months ago

Question

Simplify. Assume all variables are positive.

\newline

(27x)^{\frac{2}{3}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 8 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 7 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant