Simplify the expression below if $$ a=-2 $$ and $$ b=5 $$. $$ 7-\frac{5 a-2\left(3 a^{3} b\right)}{|a b-5|} $$

Question

UpStudy AI · Accepted Answer

Given 
$$
E = 7-\frac{5a-2\left(3a^3b\right)}{|ab-5|}
$$
with $$ a=-2 $$ and $$ b=5 $$, we substitute these values step by step.

1. Substitute $$ a=-2 $$ and $$ b=5 $$ into the expression:
   $$
   E = 7 - \frac{5(-2) - 2\left(3(-2)^3(5)\right)}{\left|(-2)(5)-5\right|}
   $$

2. Compute the product $$ 5(-2) $$:
   $$
   5(-2) = -10
   $$

3. Compute $$ (-2)^3 $$:
   $$
   (-2)^3 = -8
   $$
   Then multiply by 3 and 5:
   $$
   3(-8)(5) = -120
   $$

4. Multiply by $$-2$$ in the numerator:
   $$
   -2(-120) = 240
   $$

5. Now, the numerator becomes:
   $$
   -10 + 240 = 230
   $$

6. Compute the denominator:
   $$
   ab - 5 = (-2)(5) - 5 = -10 - 5 = -15
   $$
   Taking the absolute value:
   $$
   | -15 | = 15
   $$

7. Substitute back into the expression:
   $$
   E = 7 - \frac{230}{15}
   $$

8. Simplify the fraction by dividing numerator and denominator by 5:
   $$
   \frac{230}{15} = \frac{46}{3}
   $$

9. Express 7 as a fraction with denominator 3:
   $$
   7 = \frac{21}{3}
   $$

10. Finally, combine the fractions:
    $$
    E = \frac{21}{3} - \frac{46}{3} = \frac{21-46}{3} = \frac{-25}{3}
    $$

The simplified expression is:
$$
-\frac{25}{3}
$$
The simplified expression is $$ -\frac{25}{3} $$.

Simplify the expression below if \( a=-2 \) and \( b=5 \). \[ 7-\frac{5 a-2\left(3 a^{3} b\right)}{|a b-5|} \]