Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$Rewrite the expression in the form k*y^(n). Write the exponent as an integer, fraction, or an exact decimal (not a mixed number). (4root(4)(y^(5)))^((1)/(2))=◻$

Rewrite the expression in the form $k \cdot y^{n}$ . $\newline$ Write the exponent as an integer, fraction, or an exact decimal (not a mixed number). $\newline$ $\left(4 \sqrt[4]{y^{5}}\right)^{\frac{1}{2}}=\square$

View step-by-step help

View step-by-step help

Powers with decimal and fractional bases

Full solution

Q. Rewrite the expression in the form

k \cdot y^{n}

.

\newline

Write the exponent as an integer, fraction, or an exact decimal (not a mixed number).

\newline

\left(4 \sqrt[4]{y^{5}}\right)^{\frac{1}{2}}=\square

Identify given expression and operations: Identify the given expression and the operations involved. $\newline$ The given expression is $(4\sqrt[4]{y^{5}})^{\frac{1}{2}}$ , which involves a fourth root and an exponentiation by $\frac{1}{2}$ .
Rewrite fourth root as exponent: Rewrite the fourth root as an exponent. $\newline$ The fourth root of $y^{5}$ can be written as $y^{\frac{5}{4}}$ because the fourth root is equivalent to raising to the power of $\frac{1}{4}$ .
Apply exponent to previous result: Apply the exponent of $\frac{1}{2}$ to the result from the previous step. $\newline$ When we raise $y^{\frac{5}{4}}$ to the power of $\frac{1}{2}$ , we multiply the exponents: $\left(\frac{5}{4}\right) \times \left(\frac{1}{2}\right) = \frac{5}{8}$ .
Combine steps to write expression: Combine the steps to write the expression in the form $k*y^{n}$ . Since there is no coefficient other than $1$ in front of the $y$ term, the expression in the required form is $y^{\frac{5}{8}}$ .

More problems from Powers with decimal and fractional bases

Question

\newline

2^2 =

Posted 1 year ago

Question

Evaluate. Write your answer as a fraction or whole number.

\newline

(\frac{1}{4})^4

Posted 9 months ago

Question

Which is equal to

9^{-61}

Posted 9 months ago

Question

\newline

Express your answer using positive exponents.

\newline

r^5 \cdot r^8

Posted 9 months ago

Question

Simplify. Express your answer using a single exponent.

\newline

(h^2)^6

\newline

Posted 9 months ago

Question

Simplify. Express your answer using positive exponents.

\newline

(9p^5)(5p^8)

\newline

Posted 9 months ago

Question

Simplify. Express your answer using positive exponents.

\newline

(2v^3)(4v)(5v)

\newline

Posted 1 year ago

Question

Simplify. Express your answer using a single exponent.

\newline

(5z^8)^2

\newline

Posted 9 months ago

Question

Simplify. Express your answer using positive exponents.

\newline

r^9 \cdot r^8 \cdot r^{\text{-}5}

\newline

Posted 9 months ago

Question

Which expression is equivalent to

6 \times 6^8

\newline

\newline

\frac{1}{6^9}

\newline

6^8

\newline

\frac{1}{6^8}

\newline

6^9

Posted 1 year ago

Related topics

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