Name Trtussinn Math 10C Radicals and Exponents - Lesson 4 Powers Review 1. Use the product law or quotient law to simplify each of the following: a. $$ p^{2} imes p^{2}=p^{2+2}=p^{4} $$ b. $$ n imes n^{2} imes n^{2}=n^{2+2}=n^{4} $$ c. $$ 2 n^{4} imes 5 n^{4}=10 n^{3} $$ d. $$ 6 k^{2} imes k=61 k^{2} $$ c. $$ 6 x imes 2 x^{2}=12 x^{2} $$ f. $$ 9 x y^{2} imes 9 x^{5} y^{2}= $$ $$ -81 x^{6} y^{4} $$ g. $$ 6 m^{3} n^{3} imes 8 m^{2} n^{3}-43 m^{3} n^{6} $$ h. $$ 3 u^{2} v^{3} imes 7 u^{2} v^{3}=21 u^{4} v^{8} $$ i. $$ a^{\frac{4}{3}} imes a^{\frac{3}{3}}-a^{\frac{7}{2}}-\frac{1}{3}=a \frac{6}{3} $$ j. $$ b^{\frac{2}{4}} imes b^{\frac{1}{4}} imes b^{\frac{2}{4}}=b^{\frac{5}{1} \cdot \frac{2}{6}}+\frac{2}{6}=6^{\frac{14}{6}} $$ k. $$ \frac{m^{4}}{m}=H^{2} $$ 1. $$ \frac{h^{4}}{h^{2}}=h^{2} $$ m. $$ \frac{6 r^{3}}{2 r}=3 r^{2} $$ n. $$ \frac{3 b^{3}}{5 b^{2}}= $$ $$ \qquad $$ * o. $$ \frac{8 m^{3} n^{3}}{2 m^{3} n}=4 n^{6} $$ p. $$ \frac{6 x^{11}}{8 x^{3}}= $$ $$ \qquad $$ $$
eq $$ q. $$ \frac{12 x^{3} y^{3}}{4 x y^{3}}=3 x^{2} y^{4} $$ r. $$ \frac{-32 x^{4} y^{12}}{8 x^{3} y^{7}}=-4 x y^{5} $$

Question

Name Trtussinn Math 10C Radicals and Exponents - Lesson 4 Powers Review 1. Use the product law or quotient law to simplify each of the following: a. $$ p^{2} 	imes p^{2}=p^{2+2}=p^{4} $$ b. $$ n 	imes n^{2} 	imes n^{2}=n^{2+2}=n^{4} $$ c. $$ 2 n^{4} 	imes 5 n^{4}=10 n^{3} $$ d. $$ 6 k^{2} 	imes k=61 k^{2} $$ c. $$ 6 x 	imes 2 x^{2}=12 x^{2} $$ f. $$ 9 x y^{2} 	imes 9 x^{5} y^{2}= $$ $$ -81 x^{6} y^{4} $$ g. $$ 6 m^{3} n^{3} 	imes 8 m^{2} n^{3}-43 m^{3} n^{6} $$ h. $$ 3 u^{2} v^{3} 	imes 7 u^{2} v^{3}=21 u^{4} v^{8} $$ i. $$ a^{\frac{4}{3}} 	imes a^{\frac{3}{3}}-a^{\frac{7}{2}}-\frac{1}{3}=a \frac{6}{3} $$ j. $$ b^{\frac{2}{4}} 	imes b^{\frac{1}{4}} 	imes b^{\frac{2}{4}}=b^{\frac{5}{1} \cdot \frac{2}{6}}+\frac{2}{6}=6^{\frac{14}{6}} $$ k. $$ \frac{m^{4}}{m}=H^{2} $$ 1. $$ \frac{h^{4}}{h^{2}}=h^{2} $$ m. $$ \frac{6 r^{3}}{2 r}=3 r^{2} $$ n. $$ \frac{3 b^{3}}{5 b^{2}}= $$ $$ \qquad $$ * o. $$ \frac{8 m^{3} n^{3}}{2 m^{3} n}=4 n^{6} $$ p. $$ \frac{6 x^{11}}{8 x^{3}}= $$ $$ \qquad $$ $$ 
eq $$ q. $$ \frac{12 x^{3} y^{3}}{4 x y^{3}}=3 x^{2} y^{4} $$ r. $$ \frac{-32 x^{4} y^{12}}{8 x^{3} y^{7}}=-4 x y^{5} $$

UpStudy AI · Accepted Answer

Let's simplify each of the expressions step by step using the product and quotient laws of exponents.

### a. 
$$
p^{2} \times p^{2} = p^{2+2} = p^{4}
$$

### b. 
$$
n \times n^{2} \times n^{2} = n^{1+2+2} = n^{5}
$$

### c. 
$$
2 n^{4} \times 5 n^{4} = (2 \times 5)(n^{4} \times n^{4}) = 10 n^{4+4} = 10 n^{8}
$$

### d. 
$$
6 k^{2} \times k = 6 k^{2+1} = 6 k^{3}
$$

### e. 
$$
6 x \times 2 x^{2} = (6 \times 2)(x^{1} \times x^{2}) = 12 x^{1+2} = 12 x^{3}
$$

### f. 
$$
9 x y^{2} \times 9 x^{5} y^{2} = (9 \times 9)(x^{1} \times x^{5})(y^{2} \times y^{2}) = 81 x^{1+5} y^{2+2} = 81 x^{6} y^{4}
$$

### g. 
$$
6 m^{3} n^{3} \times 8 m^{2} n^{3} = (6 \times 8)(m^{3} \times m^{2})(n^{3} \times n^{3}) = 48 m^{3+2} n^{3+3} = 48 m^{5} n^{6}
$$

### h. 
$$
3 u^{2} v^{3} \times 7 u^{2} v^{3} = (3 \times 7)(u^{2} \times u^{2})(v^{3} \times v^{3}) = 21 u^{2+2} v^{3+3} = 21 u^{4} v^{6}
$$

### i. 
$$
a^{\frac{4}{3}} \times a^{\frac{3}{3}} = a^{\frac{4}{3} + \frac{3}{3}} = a^{\frac{7}{3}}
$$

### j. 
$$
b^{\frac{2}{4}} \times b^{\frac{1}{4}} \times b^{\frac{2}{4}} = b^{\frac{2+1+2}{4}} = b^{\frac{5}{4}}
$$

### k. 
$$
\frac{m^{4}}{m} = m^{4-1} = m^{3}
$$

### l. 
$$
\frac{h^{4}}{h^{2}} = h^{4-2} = h^{2}
$$

### m. 
$$
\frac{6 r^{3}}{2 r} = \frac{6}{2} \cdot r^{3-1} = 3 r^{2}
$$

### n. 
$$
\frac{3 b^{3}}{5 b^{2}} = \frac{3}{5} b^{3-2} = \frac{3}{5} b^{1} = \frac{3b}{5}
$$

### o. 
$$
\frac{8 m^{3} n^{3}}{2 m^{3} n} = \frac{8}{2} \cdot \frac{m^{3}}{m^{3}} \cdot \frac{n^{3}}{n^{1}} = 4 n^{3-1} = 4 n^{2}
$$

### p. 
$$
\frac{6 x^{11}}{8 x^{3}} = \frac{6}{8} \cdot x^{11-3} = \frac{3}{4} x^{8}
$$

### q. 
$$
\frac{12 x^{3} y^{3}}{4 x y^{3}} = \frac{12}{4} \cdot \frac{x^{3}}{x^{1}} \cdot \frac{y^{3}}{y^{3}} = 3 x^{3-1} = 3 x^{2}
$$

### r. 
$$
\frac{-32 x^{4} y^{12}}{8 x^{3} y^{7}} = \frac{-32}{8} \cdot \frac{x^{4}}{x^{3}} \cdot \frac{y^{12}}{y^{7}} = -4 x^{4-3} y^{12-7} = -4 x^{1} y^{5} = -4 x y^{5}
$$

These are the simplified results for each expression. If you have any further questions or need additional assistance, feel free to ask!
Here are the simplified results for each expression: a. $$ p^{4} $$ b. $$ n^{5} $$ c. $$ 10 n^{8} $$ d. $$ 6 k^{3} $$ e. $$ 12 x^{3} $$ f. $$ 81 x^{6} y^{4} $$ g. $$ 48 m^{5} n^{6} $$ h. $$ 21 u^{4} v^{6} $$ i. $$ a^{\frac{7}{3}} $$ j. $$ b^{\frac{5}{4}} $$ k. $$ m^{3} $$ l. $$ h^{2} $$ m. $$ 3 r^{2} $$ n. $$ \frac{3b}{5} $$ o. $$ 4 n^{2} $$ p. $$ \frac{3}{4} x^{8} $$ q. $$ 3 x^{2} $$ r. $$ -4 x y^{5} $$

Name
Trtussinn
Math 10C

Radicals and Exponents - Lesson 4
Powers Review

Use the product law or quotient law to simplify each of the following:
a.
b.
c.
d.
c.
f.
g.
h.
i.
j.
k.

m.
n. *
o.
p.
q.
r.

Upstudy AI Solution

Answer

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Name Trtussinn Math 10C Radicals and Exponents - Lesson 4 Powers Review Use the product law or quotient law to simplify each of the following: a. b. c. d. c. f. g. h. i. j. k. m. n. * o. p. q. r.