Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Given
x > 0, the expression
sqrt(x^(19)) is equivalent to

x^(8)sqrt(x^(2))

x^(8)sqrtx

x^(9)sqrtx

x^(9)sqrt(x^(2))

Given $x>0$ , the expression $\sqrt{x^{19}}$ is equivalent to $\newline$ $x^{8} \sqrt{x^{2}}$ $\newline$ $x^{8} \sqrt{x}$ $\newline$ $x^{9} \sqrt{x}$ $\newline$ $x^{9} \sqrt{x^{2}}$

View step-by-step help

View step-by-step help

Simplify radical expressions with root inside the root

Full solution

Q. Given

x>0

, the expression

\sqrt{x^{19}}

is equivalent to

\newline

x^{8} \sqrt{x^{2}}

\newline

x^{8} \sqrt{x}

\newline

x^{9} \sqrt{x}

\newline

x^{9} \sqrt{x^{2}}

Express in Exponential Form: We start by expressing the square root of $x$ to the power of $19$ in exponential form. $\sqrt{x^{19}} = (x^{19})^{\frac{1}{2}}$
Apply Power to Power Rule: Next, we apply the power to power rule of exponents, which states that $(a^m)^n = a^{(m \cdot n)}$ . $\newline$ $(x^{19})^{\frac{1}{2}} = x^{\frac{19}{2}}$
Simplify the Exponent: Now, we need to simplify the exponent. The fraction $\frac{19}{2}$ can be rewritten as $9 + \frac{1}{2}$ , since $\frac{19}{2} = \frac{18}{2} + \frac{1}{2} = 9 + \frac{1}{2}$ . $\newline$ $x^{\frac{19}{2}} = x^{9 + \frac{1}{2}}$
Split Exponent into Two Parts: We can now split the exponent into two parts using the property of exponents that states $a^{(m + n)} = a^m \cdot a^n$ . $\newline$ $x^{(9 + \frac{1}{2})} = x^9 \cdot x^{\frac{1}{2}}$
Recognize Square Root: Finally, we recognize that $x^{(1/2)}$ is the square root of $x$ . $\newline$ $x^9 \cdot x^{(1/2)} = x^9 \cdot \sqrt{x}$

More problems from Simplify radical expressions with root inside the root

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 1 month 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