Respuesta :
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;
[tex]|10| = 10[/tex]
2. |-4|
Using the same law applied in (1)
[tex]|-4| = 4[/tex]
3. 5/8 - 3/8 = ?
Take LCM
[tex]= \frac{5 - 3}{8}[/tex]
Subtract the numerator
[tex]= \frac{2}{8}[/tex]
Divide the numerator and denominator by 2
[tex]= \frac{1}{4}[/tex]
Hence:
[tex]\frac{5}{8} - \frac{3}{8} = \frac{1}{4}[/tex]
4. 7/8 - 5/6
Take LCM
[tex]= \frac{21 - 20}{24}[/tex]
[tex]= \frac{1}{24}[/tex]
Hence;
[tex]\frac{7}{8} - \frac{5}{6} = \frac{1}{24}[/tex]
5. 6 * (-7/2)
[tex]= 6 * \frac{-7}{2}[/tex]
Multiply the numerator
[tex]= \frac{-42}{2}[/tex]
[tex]= -21[/tex]
Hence:
[tex]6 * \frac{-7}{2} = -21[/tex]
5. 6/5 /(-12/25)
[tex]= \frac{6}{5} / \frac{-12}{25}[/tex]
Change the divide to multiplication
[tex]= \frac{6}{5} * \frac{-25}{12}[/tex]
Divide 6 and 12 by 6
[tex]= \frac{1}{5} * \frac{-25}{2}[/tex]
Divide 5 and 25 by 5
[tex]= \frac{1}{1} * \frac{-5}{2}[/tex]
[tex]= \frac{-5}{2}[/tex]
Hence;
[tex]\frac{6}{5} / \frac{-12}{25} = \frac{-5}{2}[/tex]
6. 3 + 4^2 * 2
[tex]= 3 + 4^2 * 2[/tex]
Solve the exponent
[tex]= 3 + 16 * 2[/tex]
Apply B.O.D.M.A.S
[tex]= 3 + 32[/tex]
[tex]= 35[/tex]
[tex]3 + 4^2 * 2 = 35[/tex]
7. 2/3 + 5/6
[tex]= \frac{2}{3} + \frac{5}{6}[/tex]
Apply LCM
[tex]= \frac{4 + 5}{6}[/tex]
[tex]= \frac{9}{6}[/tex]
Divide the numerator and denominator by 3
[tex]= \frac{3}{2}[/tex]
Convert to mixed fraction
[tex]= 1\frac{1}{2}[/tex]
Hence;
[tex]\frac{2}{3} + \frac{5}{6} = 1\frac{1}{2}[/tex]
8. 16 - 12/(-4)
[tex]= 16 - \frac{12}{-4}[/tex]
Solve the fraction
[tex]= 16 - (-3)[/tex]
Open the bracket
[tex]= 16 + 3[/tex]
[tex]= 19[/tex]
Hence;
[tex]16 - \frac{12}{-4} = 19[/tex]
9. -9(3w + x + 2)
[tex]= -9(3w + x + 2)[/tex]
Open brackets: Distributive property
[tex]= -9*3w -9* x -9 * 2[/tex]
[tex]= -27w -9 x -18[/tex]
Hence;
[tex]-9(3w + x + 2) = -27w -9 x -18[/tex]
10. -2(w + 2) + 5w
[tex]= -2(w + 2) + 5w[/tex]
Open bracket: using distributive property
[tex]= -2*w -2 * 2 + 5w[/tex]
[tex]= -2w -4 + 5w[/tex]
Collect Like Terms
[tex]= 5w-2w -4[/tex]
[tex]= 3w -4[/tex]
Hence;
[tex]-2(w + 2) + 5w = 3w- 4[/tex]
11. 16x^2 + 8 + 10x + 2x^2 + 14x
[tex]= 16x^2 + 8 + 10x + 2x^2 + 14x[/tex]
Collect Like Terms
[tex]= 16x^2 + 2x^2 + 10x + 14x+ 8[/tex]
[tex]= 18x^2 + 24x + 8[/tex]
Expand the expression
[tex]= 18x^2 + 12x + 12x + 8[/tex]
Factorize:
[tex]= 6x(3x + 2) + 4(3x +2)[/tex]
[tex]= (6x + 4)(3x +2)[/tex]
Hence;
[tex]16x^2 + 8 + 10x + 2x^2 + 14x = (6x + 4)(3x +2)[/tex]
12. b = -5 and y = 6
[tex]b + 9y =?[/tex]
Substitute -5 for b and 6 for y
[tex]= -5 + 9 * 6[/tex]
[tex]= -5 + 54[/tex]
[tex]= 49[/tex]
Hence;
[tex]b + 9y = 49[/tex]
13. y = -3
[tex]y^2 + 5y + 4 =?[/tex]
Substitute -3 for y
[tex]= (-3)^2 + 5(-3) + 4[/tex]
Open all brackets
[tex]= 9 -15 + 4[/tex]
[tex]= -2[/tex]
Hence;
[tex]y^2 + 5y + 4 = -2[/tex]
14.
[tex](-4)^3[/tex]
Open bracket:
[tex]= -4 * -4 * -4[/tex]
[tex]= -64[/tex]
Hence;
[tex](-4)^3 = -64[/tex]
[tex](-7)^2[/tex]
Open bracket:
[tex]= -7 * -7[/tex]
[tex]= 49[/tex]
Hence;
[tex](-7)^2 = 49[/tex]
15. Express as fractions:
[tex]\frac{3}{5^3}[/tex]
Evaluate the denominator
[tex]= \frac{3}{125}[/tex]
Hence:
[tex]\frac{3}{5^3} = \frac{3}{125}[/tex]
[tex](\frac{-1}{3})^2[/tex]
Evaluate the exponent
[tex]= (\frac{-1}{3})*(\frac{-1}{3})[/tex]
[tex]=\frac{1}{9}[/tex]
Hence:
[tex](\frac{-1}{3})^2=\frac{1}{9}[/tex]
16. Evaluate
[tex](-7)^0 =[/tex]
Evaluate the exponent
[tex](-7)^0 = 1[/tex]
[tex]2 * (1/3)^0[/tex]
Evaluate the exponent
[tex]= 2 * 1[/tex]
[tex]= 2[/tex]
Hence;
[tex]2 * (1/3)^0 = 2[/tex]
17. Evaluate
[tex]3v^2(-5v^4)[/tex]
Open bracket
[tex]= 3 * v^2*-5* v^4[/tex]
Reorder
[tex]= 3 *-5* v^4 * v^2[/tex]
[tex]= -15* v^4 * v^2[/tex]
Apply law of indices
[tex]= -15* v^{4 +2}[/tex]
[tex]= -15* v^6[/tex]
[tex]= -15v^6[/tex]
Hence:
[tex]3v^2(-5v^4) = -15v^6[/tex]
18.
[tex]2y^2w^4*6y*2w^8[/tex]
Rewrite as
[tex]2 *y^2 * w^4*6 * y*2 * w^8[/tex]
Reorder the terms
[tex]=2*6 * w^4 * w^8*y^2 * y*2[/tex]
[tex]=12 * w^4 * w^8*y^2 * y*2[/tex]
Apply law of indices
[tex]=12 * w^{4+8} *y^{2+2}[/tex]
[tex]=12 * w^{12} *y^4[/tex]
[tex]=12 w^{12} y^4[/tex]
Hence:
[tex]2y^2w^4*6y*2w^8 =12 w^{12} y^4[/tex]
19.
[tex](\frac{4p^3}{3p^7})^{-2}[/tex]
Apply law of indices
[tex]= (\frac{4p^{3-7}}{3})^{-2}[/tex]
[tex]= (\frac{4p^{-4}}{3})^{-2}[/tex]
Apply law of indices
[tex]= (\frac{4}{3p^4})^{-2}[/tex]
Apply law of indices
[tex]= (\frac{3p^4}{4})^{2}[/tex]
[tex]= (\frac{3p^4}{4}) * (\frac{3p^4}{4})[/tex]
Evaluate
[tex]= \frac{9p^8}{16}[/tex]
Hence;
[tex](\frac{4p^3}{3p^7})^{-2} = \frac{9p^8}{16}[/tex]
20.
[tex]\frac{x^{-2}}{x^{-3}}[/tex]
Apply law of indices
[tex]= x^{-2 - (-3)}[/tex]
[tex]= x^{-2 +3}[/tex]
[tex]= x^1[/tex]
[tex]= x[/tex]
Hence:
[tex]\frac{x^{-2}}{x^{-3}} =x[/tex]
