Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

4^(2x)=(1)/(32)

$4^{2 x}=\frac{1}{32}$

View step-by-step help

View step-by-step help

Evaluate integers raised to positive rational exponents

Full solution

Q.

4^{2 x}=\frac{1}{32}

Identify base and exponent: Identify the base and the exponent in the equation $4^{2x} = \frac{1}{32}$ .
Express as power of $2$ : Express $\frac{1}{32}$ as a power of $2$ , since $32$ is $2^5$ , so $\frac{1}{32}$ is $2^{-5}$ .
Rewrite equation with same bases: Rewrite the equation with the bases as the same number: $4^{2x} = 2^{-5}$ .
Apply power of a power rule: Since $4$ is $2^2$ , rewrite the left side of the equation as $(2^2)^{2x}$ .
Solve for $x$ : Apply the power of a power rule: $(a^b)^c = a^{(b*c)}$ . So, $(2^2)^{2x} = 2^{4x}$ .
Solve for x: Apply the power of a power rule: $(a^b)^c = a^{(b*c)}$ . So, $(2^2)^{2x} = 2^{4x}$ .Now we have $2^{4x} = 2^{-5}$ . The bases are the same, so the exponents must be equal: $4x = -5$ .
Solve for x: Apply the power of a power rule: $(a^b)^c = a^{(b*c)}$ . So, $(2^2)^{(2x)} = 2^{(4x)}$ .Now we have $2^{(4x)} = 2^{-5}$ . The bases are the same, so the exponents must be equal: $4x = -5$ .Divide both sides by $4$ to solve for x: $x = -\frac{5}{4}$ .

More problems from Evaluate integers raised to positive rational exponents

Question

\newline

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

\newline

Posted 3 months ago

Question

\newline

(-32)^{1/5}

\newline

Posted 3 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 3 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 2 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 3 months ago

Question

\newline

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

\newline

Posted 2 months ago

Question

\newline

32^{(-1/5)}

Posted 2 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 3 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 2 months ago