Question

simplify.

1. $sqrt4{81}$
2. $sqrt3{-27}$
3. $sqrt3{64}$
4. $sqrt3{-64}$
5. write $7y = \frac{3}{8}x - 1$ in standard form.
6. simplify $\frac{12x^2 - 16x}{16xy}$.

Explanation:

Step1: Rewrite radicand as power

$\sqrt[4]{81} = \sqrt[4]{3^4}$

Step2: Simplify 4th root

$\sqrt[4]{3^4} = 3$

Step1: Rewrite radicand as power

$\sqrt[3]{-27} = \sqrt[3]{(-3)^3}$

Step2: Simplify cube root

$\sqrt[3]{(-3)^3} = -3$

Step1: Rewrite radicand as power

$\sqrt[3]{64} = \sqrt[3]{4^3}$

Step2: Simplify cube root

$\sqrt[3]{4^3} = 4$

Step1: Rewrite radicand as power

$\sqrt[3]{-64} = \sqrt[3]{(-4)^3}$

Step2: Simplify cube root

$\sqrt[3]{(-4)^3} = -4$

Step1: Eliminate fraction (multiply by 8)

$8\times7y = 8\times\frac{3}{8}x - 8\times1$
$56y = 3x - 8$

Step2: Rearrange to standard form $Ax+By=C$

$3x - 56y = 8$

Step1: Factor numerator

$12x^2 - 16x = 4x(3x - 4)$

Step2: Cancel common factors

$\frac{4x(3x - 4)}{16xy} = \frac{3x - 4}{4y}$

Answer:

1. $3$
2. $-3$
3. $4$
4. $-4$
5. $3x - 56y = 8$
6. $\frac{3x - 4}{4y}$