Question

write the following in standard form.

1. $8.12 \times 10^{-3}$
2. $6.2 \times 10^{-4}$
3. $9.13e9$
4. simplify

$\frac{(-10)^7}{(-10)^6}$

1. simplify

$(2^3)^2$

1. solve $3^2 \cdot 4^2$
2. how many times greater is 513 than 9?
3. identify the slope and y-intercept of this table.

slope (m) ________ y-int:_______

1. solve for x.

$2x + 8 - 6x = -2(-2x + 12)$

1. solve for x.

$5(x-2) - 7x = -2(x + 3) - 4$

Explanation:

Step1: Convert to standard form

$8.12 \times 10^{-3} = 0.00812$

Step2: Convert to standard form

$6.2 \times 10^{-4} = 0.00062$

Step3: Convert E notation to standard form

$9.13\text{E}9 = 9.13 \times 10^9 = 9130000000$

Step4: Simplify using exponent rule

$\frac{(-10)^7}{(-10)^6} = (-10)^{7-6} = -10$

Step5: Simplify using power of power rule

$(2^3)^2 = 2^{3 \times 2} = 2^6 = 64$

Step6: Evaluate exponents then multiply

$3^2 \cdot 4^2 = 9 \cdot 16 = 144$

Step7: Divide to find factor

$\frac{513}{9} = 57$

Step8: Calculate slope from table

$m = \frac{3 - (-5)}{0 - (-2)} = \frac{8}{2} = 4$

Step9: Identify y-intercept from table

When $x=0$, $y=3$, so y-int = 3

Step10: Simplify and solve for x

$2x + 8 - 6x = -2(-2x + 12)$
$-4x + 8 = 4x - 24$
$8 + 24 = 4x + 4x$
$32 = 8x$
$x = 4$

Step11: Simplify and solve for x

$5(x-2) - 7x = -2(x+3) - 4$
$5x - 10 - 7x = -2x - 6 - 4$
$-2x - 10 = -2x - 10$
$0=0$ (infinitely many solutions)

Answer:

1. $0.00812$
2. $0.00062$
3. $9130000000$
4. $-10$
5. $64$
6. $144$
7. $57$
8. Slope $(m) = 4$, y-int: $3$
9. $x = 4$
10. Infinitely many real solutions