1.4.1.1: 1.4.1 and 1.4.2 Exercises

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Leah Griffith, Veronica Holbrook, Johnny Johnson & Nancy Garcia
Rio Hondo College

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Section 1.4.1 and 1.4.2 Exercises

Rewrite each expression using exponents.
1. \( 3 \cdot 3 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \)
2. \( (2.45)(2.45)(2.45)(2.45)(2.45)\)
Rewrite these expressions with positive exponents only. Then evaluate the expression.
1. \(5^{-2} \)
2. \( \dfrac{1}{5^{-2}} \)
3. \( \dfrac{3 \cdot 5}{5^{-2}}\)
Evaluate:
1. 47\(^0\)+ 5
2. \( (5.2+5.97)^{0} \)
3. \( -3(5^{1}-4\cdot 2^{0})\)
Write these numbers in order by size: \(-5^2, 5^{-2}, (5)^2, -5^{-2} \)
Evaluate:
1. \( 3^6 \cdot 3^{-3}\)
2. \( \dfrac{4^{-2}}{4^{-3}} \)
Evaluate. Write the results as a fraction and as a decimal.
1. 10\(^{-5}\)
2. 5\(^{-2}\)
3. (-2)\(^{-3}\)
4. 6\(\times 10^{-2}\)
5. \(\dfrac{16}{[(4\times 10^{-2}) - (2 \times 10^{-2})]}\)
Are any of these the same: 4\(^{-2}\) , (-4)\(^{-2}\) , -4\(^2\) ,(-4)\(^2\) ,(1/4)\(^{-2}\) , (-1/4)\(^2\)
Evaluate for \(x=2, y=3,\) and \(z=5\).
1. \( (4x^{2}y^{3})\cdot (3x^{-3}y^{-2}) \)
2. \( \dfrac{24x^{-2}y^{3}}{6x^{3}y^{-1}}\)
3. \( \left(\dfrac{2x^{-2}y^{-3}}{z^{2}} \right) \)
Complete the following:
1. Show why \((2^3)^2=2^{3\cdot 2} \).
2. Show why \((2\cdot 3)^2=2^{2}\cdot 3^{2} \).
3. Show why\( \left(\dfrac{2}{3} \right)^{2}=\dfrac{2^2}{3^2} \)