Question

Please show all of the steps to solve the Algebra math problems below.Evaluate the following.|10| = |-4| =Subtract. Write your answer as a fraction in simplest form.5/8 � 3/8 =Subtract.7/8 � 5/6Write your answer as a fraction in simplest form.Multiply.6*(-7/2) =Write your answer in simplest form.Divide. Write your answer as a fraction or mixed number in simplest form.6/5 / (- 12/25) =Evaluate.3 + 4^2 * 2 =Evaluate.2/3 + 5/6 * � =Write your answer in simplest form.Evaluate-16 - 12 / (-4) =Use the distributive property to remove the parentheses.-9(3w � x � 2) =Simplify.-2(w + 2) + 5w =Simplify the following expression.16x^2 + 8 � 10x � 2x^2 � 14x =Evaluate the expression when b = -5 and y = 6b � 9y =Evaluate the expression when y = -3Y^2 + 5y � 4 =Evaluate.(-4)^3 =(-7)^2 =Evaluate. Write your answers as fractions.3/5^3 =(-1/3)^2 =Evaluate the expressions.(-7)^0 =2(1/3)^0 = Multiply.3v^2(-5v^4) =Simplify your answer as much as possible.Multiply.2y^2w^4*6y*2w^8 =Simplify your answer as much as possible.Simplify.(4p^3/3p^7)^-2 =Write your answer using only positive exponents.Simplify.X^-2/x^-3 =Write your answer with a positive exponent only.

Answer 1

Answer:

See Explanation

Step-by-step explanation:

Please note that I'll replace all � with +

1. |10|

This implies the absolute value of 10 and it always returns the positive value;

Hence;

$|10| = 10$

2. |-4|

Using the same law applied in (1)

$|-4| = 4$

3.  5/8 - 3/8 = ?

Take LCM

$= \frac{5 - 3}{8}$

Subtract the numerator

$= \frac{2}{8}$

Divide the numerator and denominator by 2

$= \frac{1}{4}$

Hence:

$\frac{5}{8} - \frac{3}{8} = \frac{1}{4}$

4. 7/8 - 5/6

Take LCM

$= \frac{21 - 20}{24}$

$= \frac{1}{24}$

Hence;

$\frac{7}{8} - \frac{5}{6} = \frac{1}{24}$

5. 6 * (-7/2)

$= 6 * \frac{-7}{2}$

Multiply the numerator

$= \frac{-42}{2}$

$= -21$

Hence:

$6 * \frac{-7}{2} = -21$

5. 6/5 /(-12/25)

$= \frac{6}{5} / \frac{-12}{25}$

Change the divide to multiplication

$= \frac{6}{5} * \frac{-25}{12}$

Divide 6 and 12 by 6

$= \frac{1}{5} * \frac{-25}{2}$

Divide 5 and 25 by 5

$= \frac{1}{1} * \frac{-5}{2}$

$= \frac{-5}{2}$

Hence;

$\frac{6}{5} / \frac{-12}{25} = \frac{-5}{2}$

6.  3 + 4^2  * 2

$= 3 + 4^2 * 2$

Solve the exponent

$= 3 + 16 * 2$

Apply B.O.D.M.A.S

$= 3 + 32$

$= 35$

$3 + 4^2 * 2 = 35$

7.  2/3 + 5/6

$= \frac{2}{3} + \frac{5}{6}$

Apply LCM

$= \frac{4 + 5}{6}$

$= \frac{9}{6}$

Divide the numerator and denominator by 3

$= \frac{3}{2}$

Convert to mixed fraction

$= 1\frac{1}{2}$

Hence;

$\frac{2}{3} + \frac{5}{6} = 1\frac{1}{2}$

8.  16 - 12/(-4)

$= 16 - \frac{12}{-4}$

Solve the fraction

$= 16 - (-3)$

Open the bracket

$= 16 + 3$

$= 19$

Hence;

$16 - \frac{12}{-4} = 19$

9.   -9(3w + x + 2)

$= -9(3w + x + 2)$

Open brackets: Distributive property

$= -9*3w -9* x -9 * 2$

$= -27w -9 x -18$

Hence;

$-9(3w + x + 2) = -27w -9 x -18$

10.  -2(w + 2) + 5w

$= -2(w + 2) + 5w$

Open bracket: using distributive property

$= -2*w -2 * 2 + 5w$

$= -2w -4 + 5w$

Collect Like Terms

$= 5w-2w -4$

$= 3w -4$

Hence;

$-2(w + 2) + 5w = 3w- 4$

11.   16x^2 + 8 + 10x + 2x^2 + 14x

$= 16x^2 + 8 + 10x + 2x^2 + 14x$

Collect Like Terms

$= 16x^2 + 2x^2 + 10x + 14x+ 8$

$= 18x^2 + 24x + 8$

Expand the expression

$= 18x^2 + 12x + 12x + 8$

Factorize:

$= 6x(3x + 2) + 4(3x +2)$

$= (6x + 4)(3x +2)$

Hence;

$16x^2 + 8 + 10x + 2x^2 + 14x = (6x + 4)(3x +2)$

12. b = -5 and y = 6

$b + 9y =?$

Substitute -5 for b and 6 for y

$= -5 + 9 * 6$

$= -5 + 54$

$= 49$

Hence;

$b + 9y = 49$

13.    y = -3

$y^2 + 5y + 4 =?$

Substitute -3 for y

$= (-3)^2 + 5(-3) + 4$

Open all brackets

$= 9 -15 + 4$

$= -2$

Hence;

$y^2 + 5y + 4 = -2$

14.  

$(-4)^3$

Open bracket:

$= -4 * -4 * -4$

$= -64$

Hence;

$(-4)^3 = -64$

$(-7)^2$

Open bracket:

$= -7 * -7$

$= 49$

Hence;

$(-7)^2 = 49$

15.  Express as fractions:

$\frac{3}{5^3}$

Evaluate the denominator

$= \frac{3}{125}$

Hence:

$\frac{3}{5^3} = \frac{3}{125}$

$(\frac{-1}{3})^2$

Evaluate the exponent

$= (\frac{-1}{3})*(\frac{-1}{3})$

$=\frac{1}{9}$

Hence:

$(\frac{-1}{3})^2=\frac{1}{9}$

16. Evaluate

$(-7)^0 =$

Evaluate the exponent

$(-7)^0 = 1$

$2 * (1/3)^0$

Evaluate the exponent

$= 2 * 1$

$= 2$

Hence;

$2 * (1/3)^0 = 2$

17. Evaluate

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

Open bracket

$= 3 * v^2*-5* v^4$

Reorder

$= 3 *-5* v^4 * v^2$

$= -15* v^4 * v^2$

Apply law of indices

$= -15* v^{4 +2}$

$= -15* v^6$

$= -15v^6$

Hence:

$3v^2(-5v^4) = -15v^6$

18.

$2y^2w^4*6y*2w^8$

Rewrite as

$2 *y^2 * w^4*6 * y*2 * w^8$

Reorder the terms

$=2*6 * w^4 * w^8*y^2 * y*2$

$=12 * w^4 * w^8*y^2 * y*2$

Apply law of indices

$=12 * w^{4+8} *y^{2+2}$

$=12 * w^{12} *y^4$

$=12 w^{12} y^4$

Hence:

$2y^2w^4*6y*2w^8 =12 w^{12} y^4$

19.

$(\frac{4p^3}{3p^7})^{-2}$

Apply law of indices

$= (\frac{4p^{3-7}}{3})^{-2}$

$= (\frac{4p^{-4}}{3})^{-2}$

Apply law of indices

$= (\frac{4}{3p^4})^{-2}$

Apply law of indices

$= (\frac{3p^4}{4})^{2}$

$= (\frac{3p^4}{4}) * (\frac{3p^4}{4})$

Evaluate

$= \frac{9p^8}{16}$

Hence;

$(\frac{4p^3}{3p^7})^{-2} = \frac{9p^8}{16}$

20.

$\frac{x^{-2}}{x^{-3}}$

Apply law of indices

$= x^{-2 - (-3)}$

$= x^{-2 +3}$

$= x^1$

$= x$

Hence:

$\frac{x^{-2}}{x^{-3}} =x$