Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$Express the following fraction in simplest form, only using positive exponents. ((-5w^(-5))^(2))/(-5w^(-2)) Answer:$

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{\left(-5 w^{-5}\right)^{2}}{-5 w^{-2}}$ $\newline$ 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, only using positive exponents.

\newline

\frac{\left(-5 w^{-5}\right)^{2}}{-5 w^{-2}}

\newline

Answer:

Apply Power to Numerator: Apply the power to the numerator. $\newline$ When raising a power to a power, you multiply the exponents. In this case, we have $(-5w^{-5})^2$ , which means we need to square both $-5$ and $w^{-5}$ . $\newline$ $((-5)^2 \cdot (w^{-5})^2) = (25 \cdot w^{-10})$
Rewrite Denominator with Positive Exponents: Rewrite the denominator with positive exponents. $\newline$ To convert a negative exponent to a positive exponent, you take the reciprocal of the base. So, $-5w^{-2}$ becomes $-\frac{5}{w^2}$ .
Combine Numerator and Denominator: Combine the numerator and denominator. $\newline$ Now we have $(25 \cdot w^{-10}) / (-5/w^2)$ . To divide by a fraction, you multiply by its reciprocal. So, we multiply $25 \cdot w^{-10}$ by $w^2/-5$ . $\newline$ $(25 \cdot w^{-10}) \cdot (w^2/-5)$
Simplify the Expression: Simplify the expression. $\newline$ We can cancel out the $-5$ in the numerator and denominator and multiply the $w$ terms by adding the exponents. $\newline$ $(25/-5) \times (w^{(-10)} \times w^2) = -5 \times w^{(-10+2)} = -5 \times w^{(-8)}$
Rewrite with Positive Exponents: Rewrite the expression with positive exponents. $\newline$ To make the exponent of $w$ positive, we take the reciprocal of $w^{-8}$ , which gives us $w^8$ in the denominator. $\newline$ $-\frac{5}{w^8}$

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