Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

c.
2^(-3)*◻^(3)=10◻

c. $2^{-3} \cdot \square^{3}=10 \square$

View step-by-step help

View step-by-step help

Multiplication with rational exponents

Full solution

Q. c.

2^{-3} \cdot \square^{3}=10 \square

Evaluate $2^{-3}$ : Step $1$ : Evaluate $2^{-3}$ .\ Calculate $2^{-3} = \frac{1}{2^3} = \frac{1}{8}$ .
Substitute $\frac{1}{8}$ : Step $2$ : Substitute $\frac{1}{8}$ into the equation. $\newline$ Replace $2^{-3}$ with $\frac{1}{8}$ in the equation: $\newline$ $\frac{1}{8} \times ◻^{3} = 10◻$ .
Isolate $◻^3$ : Step $3$ : Isolate $◻^3$ . Multiply both sides by $8$ to clear the fraction: $◻^3 = 80◻$ .
Simplify the equation: Step $4$ : Simplify the equation. $\newline$ Divide both sides by $\square$ , assuming $\square$ is not zero: $\newline$ $\square^{2} = 80$ .
Solve for $\square$ : Step $5$ : Solve for $\square$ . $\newline$ Take the square root of both sides: $\newline$ $\square = \sqrt{80}$ . $\newline$ Simplify $\sqrt{80}$ to $4\sqrt{5}$ .

More problems from Multiplication with rational exponents

Question

\newline

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

\newline

Posted 2 months ago

Question

\newline

(-32)^{1/5}

\newline

Posted 2 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 2 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 1 month 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 2 months ago

Question

\newline

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

\newline

Posted 1 month ago

Question

\newline

32^{(-1/5)}

Posted 1 month 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 2 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 2 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 1 month ago