Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If
4^(a)=root(6)(4), what is the value of
a ?

If $4^{a}=\sqrt[6]{4}$ , what is the value of $a ?$

View step-by-step help

View step-by-step help

Solve equations using cube roots

Full solution

Q. If

4^{a}=\sqrt[6]{4}

, what is the value of

a ?

Identify Equation: We are given the equation $4^{a} = \sqrt[6]{4}$ . To find the value of $a$ , we need to express both sides of the equation with the same base if possible.
Express with Same Base: The sixth root of $4$ can be written as $4^{\frac{1}{6}}$ . So, we can rewrite the equation as $4^{a} = 4^{\frac{1}{6}}$ .
Set Exponents Equal: Since the bases are the same $4$ , we can set the exponents equal to each other. This gives us $a = \frac{1}{6}$ .
Find Value of a: We have found the value of $a$ without any need for further simplification. Therefore, $a = \frac{1}{6}$ .

More problems from Solve equations using cube roots

Question

\sqrt{49}

?

\newline

Posted 1 month ago

Question

Complete the following statement. Use the integers that are closest to the number in the middle.

\newline

<

\sqrt{40}

<

Posted 1 month ago

Question

-\sqrt{64}

\newline

Posted 2 months ago

Question

\sqrt[3]{27}

Posted 1 month ago

Question

Which two integers is

-\sqrt{48}

\newline

\newline

[A]-6 \text{ and } -5

\newline

[B]5 \text{ and } 6

\newline

[C]-7 \text{ and } -6

\newline

[D]6 \text{ and } 7

Posted 6 days ago

Question

What is the cube root of

-64

\newline

Posted 2 months ago

Question

Which two integers is

\sqrt[3]{22}

\newline

\newline

[1 \text{ and } 2]

\newline

[15 \text{ and } 16]

\newline

[16 \text{ and } 17]

\newline

[2 \text{ and } 3]

Posted 2 months ago

Question

\newline

(\sqrt{25})^2 = \_\_\_\_\_

Posted 1 month ago

Question

Look at this equation:

\newline

c^3 = 27

\newline

\newline

c

, the cube root of

27

\newline

c =

\newline

Posted 2 months ago

Question

Write the sentence as an equation.

\newline

172

is equal to the quotient of

x

4

\newline

/

) if you want to use a division sign.

\newline

Posted 1 month ago