WURKSHEET 2: Exponent Laws 1. Using exponent law 1 , simplify each of the following. Write the questions and answers down. $$ \begin{array}{ll} ext { a. } x^{2} imes x^{2} & ext { i. } a^{4} b imes b^{4} a^{3} imes 5 a b \ ext { b. } x^{2} \cdot x^{4} & ext { j. } x^{2} x^{2} x^{2} y^{4} y^{4} y^{4} \ ext { c. } a^{3} \cdot a^{5} & ext { k. } 2^{3} imes 2^{4} \ ext { d. } a^{3} \cdot x^{2} & ext { I. } 3^{4} imes 3^{5} \ ext { e. } 2 x^{2} \cdot 4 x^{5} & ext { m. }(-2)^{2} imes(-2)^{3} \ ext { f. } x^{2} y^{3} a^{4} imes y^{4} a x^{8} & ext { n. } 3 a^{2} imes-2 a^{3} imes 4 a^{5} \ ext { g. }\left(x^{2} y^{3} a^{4} b ight) imes\left(y^{4} a b x^{8} ight) & ext { o. } x^{2} imes x^{-5} \ ext { h. }-2 x^{2} \cdot-3 x^{2} \cdot-4 x^{2} & \end{array} $$

Question

WURKSHEET 2: Exponent Laws 1. Using exponent law 1 , simplify each of the following. Write the questions and answers down. $$ \begin{array}{ll}	ext { a. } x^{2} 	imes x^{2} & 	ext { i. } a^{4} b 	imes b^{4} a^{3} 	imes 5 a b \ 	ext { b. } x^{2} \cdot x^{4} & 	ext { j. } x^{2} x^{2} x^{2} y^{4} y^{4} y^{4} \ 	ext { c. } a^{3} \cdot a^{5} & 	ext { k. } 2^{3} 	imes 2^{4} \ 	ext { d. } a^{3} \cdot x^{2} & 	ext { I. } 3^{4} 	imes 3^{5} \ 	ext { e. } 2 x^{2} \cdot 4 x^{5} & 	ext { m. }(-2)^{2} 	imes(-2)^{3} \ 	ext { f. } x^{2} y^{3} a^{4} 	imes y^{4} a x^{8} & 	ext { n. } 3 a^{2} 	imes-2 a^{3} 	imes 4 a^{5} \ 	ext { g. }\left(x^{2} y^{3} a^{4} bight) 	imes\left(y^{4} a b x^{8}ight) & 	ext { o. } x^{2} 	imes x^{-5} \ 	ext { h. }-2 x^{2} \cdot-3 x^{2} \cdot-4 x^{2} & \end{array} $$

UpStudy AI · Accepted Answer

**a.**  
$$
x^{2} \times x^{2} = x^{2+2} = x^{4}
$$

**b.**  
$$
x^{2} \times x^{4} = x^{2+4} = x^{6}
$$

**c.**  
$$
a^{3} \times a^{5} = a^{3+5} = a^{8}
$$

**d.**  
Since the bases are different, the expression remains the same:  
$$
a^{3} \times x^{2} = a^3x^2
$$

**e.**  
Multiply the coefficients and add the exponents of $$x$$:  
$$
2 \times 4 = 8,\quad x^{2} \times x^{5} = x^{2+5} = x^{7}
$$  
Thus,  
$$
2x^{2} \times 4x^{5} = 8x^{7}
$$

**f.**  
Group like bases together:
- For $$a$$: $$a^4 \times a = a^{4+1} = a^{5}$$  
- For $$x$$: $$x^{2} \times x^{8} = x^{2+8} = x^{10}$$  
- For $$y$$: $$y^{3} \times y^{4} = y^{3+4} = y^{7}$$

Thus,  
$$
x^{2}y^{3}a^{4} \times y^{4}ax^{8} = a^{5}x^{10}y^{7}
$$

**g.**  
Group like bases:
- For $$x$$: $$x^{2} \times x^{8} = x^{2+8} = x^{10}$$  
- For $$y$$: $$y^{3} \times y^{4} = y^{3+4} = y^{7}$$  
- For $$a$$: $$a^{4} \times a = a^{4+1} = a^{5}$$  
- For $$b$$: $$b \times b = b^2$$

Thus,  
$$
\left(x^{2}y^{3}a^{4}b\right) \times \left(y^{4}abx^{8}\right) = a^{5}x^{10}y^{7}b^{2}
$$

**h.**  
Multiply the coefficients and add the exponents of $$x$$:
- Coefficients: $$-2 \times -3 = 6$$ and $$6 \times -4 = -24$$  
- For $$x$$: $$x^{2} \times x^{2} \times x^{2} = x^{2+2+2} = x^{6}$$

Thus,  
$$
-2x^{2} \times -3x^{2} \times -4x^{2} = -24x^{6}
$$

**i.**  
Multiply the coefficients and add the exponents for like bases:
- Coefficients: $$1 \times 1 \times 5 = 5$$  
- For $$a$$: $$a^{4}\times a^{3} \times a = a^{4+3+1} = a^{8}$$  
- For $$b$$: $$b \times b^{4} \times b = b^{1+4+1} = b^{6}$$

Thus,  
$$
a^{4}b \times b^{4}a^{3} \times 5ab = 5a^{8}b^{6}
$$

**j.**  
Group the $$x$$ and $$y$$ terms:
- For $$x$$: $$x^{2} \times x^{2} \times x^{2} = x^{2+2+2} = x^{6}$$  
- For $$y$$: $$y^{4} \times y^{4} \times y^{4} = y^{4+4+4} = y^{12}$$

Thus,  
$$
x^{2}x^{2}x^{2}y^{4}y^{4}y^{4} = x^{6}y^{12}
$$

**k.**  
$$
2^{3} \times 2^{4} = 2^{3+4} = 2^{7}
$$

**l.**  
$$
3^{4} \times 3^{5} = 3^{4+5} = 3^{9}
$$

**m.**  
$$
(-2)^{2} \times (-2)^{3} = (-2)^{2+3} = (-2)^{5}
$$

**n.**  
First, multiply the coefficients:
$$
3 \times (-2) \times 4 = -24
$$  
Then, add the exponents of $$a$$:
$$
a^{2} \times a^{3} \times a^{5} = a^{2+3+5} = a^{10}
$$  
Thus,  
$$
3a^{2} \times (-2a^{3}) \times 4a^{5} = -24a^{10}
$$

**o.**  
$$
x^{2} \times x^{-5} = x^{2+(-5)} = x^{-3}
$$
**a.** $$ x^{2} \times x^{2} = x^{4} $$ **b.** $$ x^{2} \times x^{4} = x^{6} $$ **c.** $$ a^{3} \times a^{5} = a^{8} $$ **d.** $$ a^{3} \times x^{2} = a^{3}x^{2} $$ **e.** $$ 2x^{2} \times 4x^{5} = 8x^{7} $$ **f.** $$ x^{2}y^{3}a^{4} \times y^{4}ax^{8} = a^{5}x^{10}y^{7} $$ **g.** $$ \left(x^{2}y^{3}a^{4}b\right) \times \left(y^{4}abx^{8}\right) = a^{5}x^{10}y^{7}b^{2} $$ **h.** $$ -2x^{2} \times -3x^{2} \times -4x^{2} = -24x^{6} $$ **i.** $$ a^{4}b \times b^{4}a^{3} \times 5ab = 5a^{8}b^{6} $$ **j.** $$ x^{2}x^{2}x^{2}y^{4}y^{4}y^{4} = x^{6}y^{12} $$ **k.** $$ 2^{3} \times 2^{4} = 2^{7} $$ **l.** $$ 3^{4} \times 3^{5} = 3^{9} $$ **m.** $$ (-2)^{2} \times (-2)^{3} = (-2)^{5} $$ **n.** $$ 3a^{2} \times (-2a^{3}) \times 4a^{5} = -24a^{10} $$ **o.** $$ x^{2} \times x^{-5} = x^{-3} $$

WURKSHEET 2: Exponent Laws

Using exponent law 1 , simplify each of the following. Write the
questions and answers down.

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WURKSHEET 2: Exponent Laws Using exponent law 1 , simplify each of the following. Write the questions and answers down.