Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

sqrt(y^(3)z)*sqrt(y^(13)z^(8))
Which of the following is equivalent to the given expression for all real values of
y and
z ?
Choose 1 answer:
(A)
y^(4)z^(3)
(B)
y^(8)z^(4)
(C)
y^(8)z^(4)sqrtz
(D)
y^(15)z^(4)sqrty

$\sqrt{y^{3} z} \cdot \sqrt{y^{13} z^{8}}$ $\newline$ Which of the following is equivalent to the given expression for all real values of $y$ and $z$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $y^{4} z^{3}$ $\newline$ (B) $y^{8} z^{4}$ $\newline$ (C) $y^{8} z^{4} \sqrt{z}$ $\newline$ (D) $y^{15} z^{4} \sqrt{y}$

View step-by-step help

View step-by-step help

Compare linear and exponential growth

Full solution

Q.

\sqrt{y^{3} z} \cdot \sqrt{y^{13} z^{8}}

\newline

Which of the following is equivalent to the given expression for all real values of

y

and

z

?

\newline

Choose

1

answer:

\newline

(A)

y^{4} z^{3}

\newline

(B)

y^{8} z^{4}

\newline

(C)

y^{8} z^{4} \sqrt{z}

\newline

(D)

y^{15} z^{4} \sqrt{y}

Property of square roots: We are given the expression $\sqrt{y^{3}z} \cdot \sqrt{y^{13}z^{8}}$ . To simplify this expression, we will use the property of square roots that $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$ .
Multiplying the square roots: Now we multiply the two square roots together: $\sqrt{y^{3}z} \times \sqrt{y^{13}z^{8}} = \sqrt{(y^{3}z) \times (y^{13}z^{8})}$ .
Combining terms under the square root: Next, we combine the terms under the square root: $\sqrt{(y^{3}z) \cdot (y^{13}z^{8})} = \sqrt{y^{3+13} \cdot z^{1+8}}$ .
Adding exponents of like bases: We add the exponents of like bases: $\sqrt{y^{(3+13)} \cdot z^{(1+8)}} = \sqrt{y^{16} \cdot z^{9}}$ .
Simplifying the square root of each term: Now we simplify the square root of each term: $\sqrt{y^{16} \cdot z^{9}} = \sqrt{y^{16}} \cdot \sqrt{z^{9}}$ .
Dividing exponents by $2$ : Since $y^{16}$ and $z^{9}$ are perfect squares, we can take the square root of each: $\sqrt{y^{16}} \cdot \sqrt{z^{9}} = y^{\frac{16}{2}} \cdot z^{\frac{9}{2}}$ .
Recognizing $z^{4.5}$ as $z^{4}\sqrt{z}$ : We simplify the exponents by dividing them by $2$ : $y^{\frac{16}{2}} \cdot z^{\frac{9}{2}} = y^{8} \cdot z^{4.5}$ .
Matching with option (C): We recognize that $z^{4.5}$ is the same as $z^{4}\sqrt{z}$ : $y^{8} \cdot z^{4.5} = y^{8} \cdot z^{4} \cdot \sqrt{z}$ .
Matching with option (C): We recognize that $z^{4.5}$ is the same as $z^{4}\sqrt{z}$ : $y^{8} \cdot z^{4.5} = y^{8} \cdot z^{4} \cdot \sqrt{z}$ . We compare our result with the given answer choices and find that it matches with option (C) $y^{8}z^{4}\sqrt{z}$ .

More problems from Compare linear and exponential growth

Question

Jill bought a used motorcycle from a seller online for $1,200. The seller will charge her $5 a day to store the motorcycle at his house until she is able to pick it up. You can use a function to describe the total amount of money Jill will owe the seller if she waits

x

days to pick up the motorcycle.

\newline

Write an equation for the function. If it is linear, write it in the form

g(x) = mx + b

. If it is exponential, write it in the form

g(x) = a(b)^x

\newline

g(x) = \underline{\hspace{3em}}

Posted 8 months ago

Question

f(t)=-2t-7

change over the interval from

t=-7

t=-6

\newline

\newline

\left[\text{f(t) decreases by } 2\right]

\newline

\left[\text{f(t) increases by } 2\right]

\newline

\left[\text{f(t) increases by } 200\%\right]

\newline

\left[\text{f(t) decreases by a factor of } 2\right]

Posted 8 months ago

Question

g(t)=9^t

change over the interval from

t=1

t=3

\newline

\newline

\left[\text{g(t) decreases by a factor of } 81\right]

\newline

\left[\text{g(t) increases by a factor of } 81\right]

\newline

\left[\text{g(t) increases by } 18\%\right]

\newline

\left[\text{g(t) decreases by } 9\%\right]

Posted 8 months ago

Question

Both of these functions grow as

x

gets larger and larger. Which function eventually exceeds the other?

\newline

\newline

(A)f(x) = 8x + 3.3

\newline

(B)g(x) = 3.3^x - 5

Posted 9 months ago

Question

Both of these functions grow as

x

gets larger and larger. Which function eventually exceeds the other?

\newline

\newline

(A) \ f(x) = 2x + 9

\newline

(B)\ g(x) = 2^x

Posted 9 months ago

Question

f(x)

g(x)

are differentiable.

\newline

h(x)

h(x)=\frac{g(x)}{f(x)}

\newline

f(8)=1

f'(8)=-6

g(8)=8

g'(8)=-10

h'(8)

\newline

Simplify any fractions.

\newline

h'(8)=

Posted 8 months ago

Question

p(x)

q(x)

are differentiable.

\newline

r(x)

r(x)= \frac{p(x)}{q(x)}

\newline

p(3)= 2

p'(3)= 4

q(3)= 6

q'(3)= 9

r'(3)

\newline

Simplify any fractions.

\newline

r'(3)=

Posted 9 months ago

Question

u(x)

v(x)

are differentiable.

\newline

w(x)

w(x)= \frac{u(x)}{v(x)}

\newline

u(5)= 3

u'(5)= -2

v(5)= 7

v'(5)= 1

w'(5)

\newline

Simplify any fractions.

\newline

w'(5)=

Posted 9 months ago

Question

a(x)

b(x)

are differentiable.

\newline

c(x)

c(x)= \frac{a(x)}{b(x)}

\newline

a(2)= 4

a'(2)= 5

b(2)= 1

b'(2)= -3

c'(2)

\newline

Simplify any fractions.

\newline

c'(2)=

Posted 9 months ago

Question

m(x)

n(x)

are differentiable.

\newline

o(x)

o(x)= \frac{m(x)}{n(x)}

\newline

m(7)= 2

m'(7)= -1

n(7)= 4

n'(7)= 8

o'(7)

\newline

Simplify any fractions.

\newline

o'(7)=

Posted 9 months ago

Related topics

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