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Simplify the following:

(a) [tex]\(\frac{2^1 \times 2^5 \times 2^8}{2^2 \times 2^4}\)[/tex]

(b) [tex]\(\frac{3^6 \times 3^2 \times 3^{-3}}{3^2 \times 3}\)[/tex]

Sagot :

GinnyAnswer
Let's solve each part step-by-step.

### Part (a)
Simplify the expression [tex]\(\frac{2^1 \times 2^5 \times 2^8}{2^2 \times 2^4}\)[/tex]:

1. Combine the powers in the numerator:
[tex]\[ 2^1 \times 2^5 \times 2^8 = 2^{1+5+8} = 2^{14} \][/tex]

2. Combine the powers in the denominator:
[tex]\[ 2^2 \times 2^4 = 2^{2+4} = 2^{6} \][/tex]

3. Simplify the fraction:
[tex]\[ \frac{2^{14}}{2^{6}} = 2^{14-6} = 2^{8} \][/tex]

Therefore, the simplified form is:
[tex]\[ 2^{8} = 256 \][/tex]

### Part (b)
Simplify the expression [tex]\(\frac{3^6 \times 3^2 \times 3^{-3}}{3^2 \times 3}\)[/tex]:

1. Combine the powers in the numerator:
[tex]\[ 3^6 \times 3^2 \times 3^{-3} = 3^{6+2-3} = 3^{5} \][/tex]

2. Combine the powers in the denominator:
[tex]\[ 3^2 \times 3 = 3^2 \times 3^1 = 3^{2+1} = 3^{3} \][/tex]

3. Simplify the fraction:
[tex]\[ \frac{3^{5}}{3^{3}} = 3^{5-3} = 3^{2} \][/tex]

Therefore, the simplified form is:
[tex]\[ 3^{2} = 9 \][/tex]

### Final Answer
(a) [tex]\(\frac{2^1 \times 2^5 \times 2^8}{2^2 \times 2^4} = 256\)[/tex]

(b) [tex]\(\frac{3^6 \times 3^2 \times 3^{-3}}{3^2 \times 3} = 9\)[/tex]
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