Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

root(3)(4^(x+1))=2sqrt(8^(x))

$\sqrt[3]{4^{x+1}}=2 \sqrt{8^{x}}$

View step-by-step help

View step-by-step help

Simplify the product of two radical expressions having same variable

Full solution

Q.

\sqrt[3]{4^{x+1}}=2 \sqrt{8^{x}}

Convert to Exponential Form: Convert the cube root and square root to exponential form: $\newline$ $\sqrt[3]{4^{x+1}} = (4^{x+1})^{\frac{1}{3}}$ $\newline$ $2\sqrt{8^{x}} = 2\cdot(8^{x})^{\frac{1}{2}}$
Simplify Exponents: Simplify the exponents: $\newline$ $(4^{(x+1)})^{\frac{1}{3}} = 4^{\frac{(x+1)}{3}}$ $\newline$ $2\cdot(8^{x})^{\frac{1}{2}} = 2\cdot(2^{3x})^{\frac{1}{2}} = 2\cdot2^{\frac{3x}{2}}$
Set Equal: Set the expressions equal to each other: $\newline$ $4^{\frac{x+1}{3}} = 2\cdot2^{\frac{3x}{2}}$
Express as $2^2$ : Express $4$ as $2^2$ and simplify: $\newline$ $(2^2)^{\frac{x+1}{3}} = 2\cdot2^{\frac{3x}{2}}$ $\newline$ $2^{2\frac{x+1}{3}} = 2^{1+\frac{3x}{2}}$
Set Exponents Equal: Since the bases are the same, set the exponents equal to each other: $\frac{2(x+1)}{3} = 1+\frac{3x}{2}$
Cross Multiply: Cross multiply to solve for $x$ : $4(x+1) = 3(1+\frac{3x}{2})$ $4x+4 = 3+\frac{9x}{2}$
Multiply by $2$ : Multiply everything by $2$ to get rid of the fraction: $\newline$ $8x+8 = 6+9x$
Subtract $8x$ : Subtract $8x$ from both sides: $\newline$ $8 = 6+x$

More problems from Simplify the product of two radical expressions having same variable

Question

Find the real-number root.

\newline

\sqrt{16}

\newline

\newline

Write your answer in simplified form.

\newline

\_\_\_\_

Posted 3 months ago

Question

Find the real-number root.

\newline

\sqrt{\frac{9}{16}}

\newline

Simplify your answer and write it as a decimal or as a proper or improper fraction.

\newline

\_\_\_\_\_

Posted 3 months ago

Question

Find the real-number root using a calculator. Round your answer to the nearest thousandth.

\newline

\newline

Posted 3 months ago

Question

Multiply. Write your answer in simplest form.

\newline

\sqrt{273} \times \sqrt{42}

\newline

Posted 2 months ago

Question

\newline

\sqrt{\frac{63}{4}}

\newline

Posted 3 months ago

Question

Simplify. Rationalize the denominator.

\newline

\frac{-4}{9 - \sqrt{2}}

\newline

Posted 3 months ago

Question

z

\newline

16 = \sqrt{z}

\newline

z =

Posted 3 months ago

Question

Simplify the radical expression.

\sqrt{14x^{14}}

Write your answer in the form

A

\sqrt{B}

A\sqrt{B}

A

B

are constants or expressions in

x

. Use at most one radical in your answer, and at most one absolute value symbol in your expression for

A

Posted 3 months ago

Question

Simplify the radical expression.

\newline

\sqrt{12x^{12}}

\newline

Write your answer in the form

A

\sqrt{B}

A\sqrt{B}

A

B

are constants or expressions in

x

. Use at most one radical in your answer, and at most one absolute value symbol in your expression for

A

\newline

\underline{\hspace{3cm}}

Posted 3 months ago

Question

What is the value of

\sin \left(\frac{5 \pi}{6}\right) ?

\newline

1

\newline

-\frac{\sqrt{3}}{2}

\newline

-\frac{\sqrt{2}}{2}

\newline

\frac{1}{2}

\newline

150

Posted 4 months ago