1) $$ 2 k^{3} $$ k) $$ (2 k)^{-3} $$ m) $$ (-2 x)^{-3} $$ i) $$ 4 x^{-1} y^{-2} $$ 0) $$ -5 x^{-3} y y^{-2} $$ P) $$ 2^{-2} x^{6} y^{-3} $$

Question

UpStudy AI · Accepted Answer

**1) $$ 2k^{3} $$**  
This expression is already simplified.

---

**k) $$ (2k)^{-3} $$**  
First, rewrite the expression using the rule $$(ab)^{-n} = a^{-n}b^{-n}$$:  
$$
(2k)^{-3} = 2^{-3}k^{-3}
$$  
Since $$2^{-3} = \frac{1}{2^3} = \frac{1}{8}$$, the simplified form is:  
$$
(2k)^{-3} = \frac{1}{8k^{3}}
$$

---

**m) $$ (-2x)^{-3} $$**  
Apply the rule $$(ab)^{-n} = a^{-n}b^{-n}$$:  
$$
(-2x)^{-3} = (-2)^{-3}x^{-3}
$$  
Calculate $$(-2)^{-3}$$:  
$$
(-2)^{-3} = \frac{1}{(-2)^{3}} = \frac{1}{-8} = -\frac{1}{8}
$$  
Thus, the simplified form is:  
$$
(-2x)^{-3} = -\frac{1}{8x^{3}}
$$

---

**i) $$ 4x^{-1}y^{-2} $$**  
Write the negative exponents as reciprocals:  
$$
4x^{-1}y^{-2} = \frac{4}{x^{1}y^{2}} = \frac{4}{xy^{2}}
$$

---

**0) $$ -5x^{-3}yy^{-2} $$**  
First, combine the $$y$$ terms. Recall that $$y = y^1$$, so:  
$$
y \cdot y^{-2} = y^{1-2} = y^{-1}
$$  
Now, the expression becomes:  
$$
-5x^{-3}y^{-1} = -\frac{5}{x^{3}y}
$$

---

**P) $$ 2^{-2}x^{6}y^{-3} $$**  
Rewrite each term:  
$$
2^{-2} = \frac{1}{2^2} = \frac{1}{4} \quad \text{and} \quad y^{-3} = \frac{1}{y^{3}}
$$  
Thus, the expression can be written as:  
$$
2^{-2}x^{6}y^{-3} = \frac{1}{4} \cdot x^{6} \cdot \frac{1}{y^{3}} = \frac{x^{6}}{4y^{3}}
$$
1) $$ 2k^{3} $$ k) $$ \frac{1}{8k^{3}} $$ m) $$ -\frac{1}{8x^{3}} $$ i) $$ \frac{4}{xy^{2}} $$ 0) $$ -\frac{5}{x^{3}y} $$ P) $$ \frac{x^{6}}{4y^{3}} $$

1) \( 2 k^{3} \) k) \( (2 k)^{-3} \) m) \( (-2 x)^{-3} \) i) \( 4 x^{-1} y^{-2} \) 0) \( -5 x^{-3} y y^{-2} \) P) \( 2^{-2} x^{6} y^{-3} \)

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Algebra Questions