Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$G(z)=(1-9z)^{2}\sqrt{z^{2}+1}$

View step-by-step help

View step-by-step help

Evaluate integers raised to rational exponents

Full solution

Q.

G(z)=(1-9z)^{2}\sqrt{z^{2}+1}

Identify Components: We are given the function $G(z)=(1-9z)^{2}\sqrt{z^{2}+1}$ . The first step is to identify the components of the function that can be simplified separately. The function consists of two parts: a binomial raised to the power of $2$ , and a square root of a binomial.
Simplify Binomial: The second step is to simplify the binomial $(1-9z)^{2}$ . This is done by squaring both terms in the binomial and combining like terms. $\newline$ $(1-9z)^{2} = (1-9z)\cdot(1-9z)$ $\newline$ $= 1^{2} - 2\cdot(1)\cdot(9z) + (9z)^{2}$ $\newline$ $= 1 - 18z + 81z^{2}$
Simplify Square Root: The third step is to simplify the square root $\sqrt{z^{2}+1}$ . Since there is no further simplification that can be done to this term, we leave it as is. $\sqrt{z^{2}+1}$ remains unchanged.
Combine Terms: The fourth step is to combine the simplified terms from step $2$ and step $3$ to write the simplified form of the function $G(z)$ . $G(z) = (1 - 18z + 81z^2) \cdot \sqrt{z^{2}+1}$ This is the simplified form of the function.

More problems from Evaluate integers raised to rational exponents

Question

\newline

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

\newline

Posted 9 months ago

Question

\newline

(-32)^{1/5}

\newline

Posted 9 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 5 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 5 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 5 months ago

Question

\newline

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

\newline

Posted 5 months ago

Question

\newline

32^{(-1/5)}

Posted 7 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 9 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 8 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 7 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant