2. $$ \frac{a^{2 x} imes a^{x} b^{-2}}{a^{3 x}} $$

Question

2. $$ \frac{a^{2 x} 	imes a^{x} b^{-2}}{a^{3 x}} $$

UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\left(a^{2x}\times a^{x}b^{-2}\right)}{\left(a^{3x}\right)}$$
- step1: Evaluate:
  $$\frac{\left(a^{2x}\times a^{x}b^{-2}\right)}{a^{3x}}$$
- step2: Remove the parentheses:
  $$\frac{a^{2x}\times a^{x}b^{-2}}{a^{3x}}$$
- step3: Multiply by $$a^{-n}:$$
  $$a^{2x}\times a^{x}b^{-2}a^{-3x}$$
- step4: Multiply the terms:
  $$a^{2x+x-3x}b^{-2}$$
- step5: Calculate:
  $$a^{0}b^{-2}$$
- step6: Evaluate the power:
  $$b^{-2}$$
- step7: Simplify:
  $$\frac{1}{b^{2}}$$
To simplify the expression $$ \frac{a^{2x} \times a^{x} b^{-2}}{a^{3x}} $$, we can follow these steps:

1. **Combine the exponents of $$ a $$** in the numerator:
   $$
   a^{2x} \times a^{x} = a^{2x + x} = a^{3x}
   $$

2. **Rewrite the expression**:
   $$
   \frac{a^{3x} b^{-2}}{a^{3x}}
   $$

3. **Cancel $$ a^{3x} $$** in the numerator and denominator:
   $$
   \frac{a^{3x}}{a^{3x}} \times b^{-2} = 1 \times b^{-2} = b^{-2}
   $$

4. **Express $$ b^{-2} $$** in terms of positive exponent:
   $$
   b^{-2} = \frac{1}{b^{2}}
   $$

Thus, the simplified expression is:
$$
\frac{1}{b^{2}}
$$
The simplified expression is $$ \frac{1}{b^{2}} $$.

2. \( \frac{a^{2 x} \times a^{x} b^{-2}}{a^{3 x}} \)

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Algebra Questions