Given x > 0 and y > 0, select the expression that is equivalent to sqrt(-16x^(8)y^(3)) -4x^(4)y^((3)/(2)) -4x^(6)y 4ix^(4)y^((3)/(2)) 4ix^(6)y

Simplify inside square root: First, we need to simplify the expression inside the square root. The square root of a negative number involves the imaginary unit i, where i^2 = -1. Therefore, we can rewrite the expression as sqrt(-1) * sqrt(16x^(8)y^(3)).Simplify square roots: Next, we can simplify the square root of -1 as i, and the square root of 16x^(8)y^(3) as 4x^(4)y^(3/2), since 16 is a perfect square and x^(8) and y^(3) have exponents that are multiples of 2.Multiply simplified expressions: Multiplying these two results together, we get i * 4x^(4)y^(3/2), which simplifies to 4ix^(4)y^(3/2).Check for correct answer: Now we need to check if our result matches any of the given options. The correct expression equivalent to sqrt(-16x^(8)y^(3)) is 4ix^(4)y^(3/2).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Given
x > 0 and
y > 0, select the expression that is equivalent to

sqrt(-16x^(8)y^(3))

-4x^(4)y^((3)/(2))

-4x^(6)y

4ix^(4)y^((3)/(2))

4ix^(6)y

Given x>0 and y>0 , select the expression that is equivalent to $\newline$ $\sqrt{-16 x^{8} y^{3}}$ $\newline$ $-4 x^{4} y^{\frac{3}{2}}$ $\newline$ $-4 x^{6} y$ $\newline$ $4 i x^{4} y^{\frac{3}{2}}$ $\newline$ $4 i x^{6} y$

View step-by-step help

Home

Math Problems

Calculus

Find indefinite integrals using the substitution

Full solution

Q. Given

x>0

and

y>0

, select the expression that is equivalent to

\newline

\sqrt{-16 x^{8} y^{3}}

\newline

-4 x^{4} y^{\frac{3}{2}}

\newline

-4 x^{6} y

\newline

4 i x^{4} y^{\frac{3}{2}}

\newline

4 i x^{6} y

Simplify inside square root: First, we need to simplify the expression inside the square root. The square root of a negative number involves the imaginary unit $i$ , where $i^2 = -1$ . Therefore, we can rewrite the expression as $\sqrt{-1} \times \sqrt{16x^{8}y^{3}}$ .
Simplify square roots: Next, we can simplify the square root of $-1$ as $i$ , and the square root of $16x^{8}y^{3}$ as $4x^{4}y^{\frac{3}{2}}$ , since $16$ is a perfect square and $x^{8}$ and $y^{3}$ have exponents that are multiples of $2$ .
Multiply simplified expressions: Multiplying these two results together, we get $i \times 4x^{4}y^{\frac{3}{2}}$ , which simplifies to $4ix^{4}y^{\frac{3}{2}}$ .
Check for correct answer: Now we need to check if our result matches any of the given options. The correct expression equivalent to $\sqrt{-16x^{8}y^{3}}$ is $4ix^{4}y^{\frac{3}{2}}$ .