CHAPTER 6 REVIEW Simplify the following expressions. Reduce to simplest form. Make all exponents positive. 1. $$ 5^{2} imes 5^{3} 55 $$ 6. $$ \left(b^{3} ight)^{-4} $$ 2. $$ \left(4^{4} ight)^{5} \cup 20 $$ 7. $$ \frac{4^{6}}{4^{4}} $$ 11. $$ 3^{3} imes 3^{2} 3^{5} $$ 16. $$ \left(5^{-9} \cdot 5^{7} ight)^{-2}=54 $$ 12. $$ \left(2^{4} ight)^{2} $$ 17. $$ \frac{\left(2^{3} ight)^{2}}{2^{4}} $$ 3. $$ \left(4 y^{3} ight)^{3} 6 y $$ 8. $$ \left(\frac{3}{5} ight)^{2} $$ 13. $$ 5^{7} imes 5^{-4} 53 $$ 18. $$ \frac{y^{-2}}{3 y^{4}} $$ 4. $$ 6 x^{-3} $$ 9. $$ \frac{\left(3 a^{2} ight)^{3}}{a^{3}} $$ 14. $$ x^{3} \cdot x^{-7} $$ 19. $$ \frac{\left(2^{3} ight)^{2}}{2^{4}} $$ 5. $$ \left(3 a^{2} ight)^{-2} $$ 10. $$ (2 x)^{-4} $$ 15. $$ \left(4^{2} ight)^{-2} $$ 20. $$ \left(4 d^{5} ight)^{-3} $$

Question

CHAPTER 6 REVIEW Simplify the following expressions. Reduce to simplest form. Make all exponents positive. 1. $$ 5^{2} 	imes 5^{3} 55 $$ 6. $$ \left(b^{3}ight)^{-4} $$ 2. $$ \left(4^{4}ight)^{5} \cup 20 $$ 7. $$ \frac{4^{6}}{4^{4}} $$ 11. $$ 3^{3} 	imes 3^{2} 3^{5} $$ 16. $$ \left(5^{-9} \cdot 5^{7}ight)^{-2}=54 $$ 12. $$ \left(2^{4}ight)^{2} $$ 17. $$ \frac{\left(2^{3}ight)^{2}}{2^{4}} $$ 3. $$ \left(4 y^{3}ight)^{3} 6 y $$ 8. $$ \left(\frac{3}{5}ight)^{2} $$ 13. $$ 5^{7} 	imes 5^{-4} 53 $$ 18. $$ \frac{y^{-2}}{3 y^{4}} $$ 4. $$ 6 x^{-3} $$ 9. $$ \frac{\left(3 a^{2}ight)^{3}}{a^{3}} $$ 14. $$ x^{3} \cdot x^{-7} $$ 19. $$ \frac{\left(2^{3}ight)^{2}}{2^{4}} $$ 5. $$ \left(3 a^{2}ight)^{-2} $$ 10. $$ (2 x)^{-4} $$ 15. $$ \left(4^{2}ight)^{-2} $$ 20. $$ \left(4 d^{5}ight)^{-3} $$

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{3}{5}ight)^{2}$$
- step1: Use the properties of exponents:
  $$\frac{3^{2}}{5^{2}}$$
- step2: Evaluate the power:
  $$\frac{9}{5^{2}}$$
- step3: Evaluate the power:
  $$\frac{9}{25}$$
Calculate or simplify the expression $$ \frac{4^{6}}{4^{4}} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{4^{6}}{4^{4}}$$
- step1: Multiply by $$a^{-n}:$$
  $$4^{6}	imes 4^{-4}$$
- step2: Multiply:
  $$4^{6-4}$$
- step3: Subtract the numbers:
  $$4^{2}$$
- step4: Evaluate the power:
  $$16$$
Calculate or simplify the expression $$ \left(4 d^{5}ight)^{-3} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(4d^{5}ight)^{-3}$$
- step1: Use the properties of exponents:
  $$4^{-3}\left(d^{5}ight)^{-3}$$
- step2: Evaluate the power:
  $$\frac{1}{64}d^{-15}$$
- step3: Simplify:
  $$\frac{1}{64d^{15}}$$
Calculate or simplify the expression $$ x^{3} \cdot x^{-7} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$x^{3}	imes x^{-7}$$
- step1: Simplify the expression:
  $$x^{3-7}$$
- step2: Subtract the numbers:
  $$x^{-4}$$
- step3: Simplify:
  $$\frac{1}{x^{4}}$$
Calculate or simplify the expression $$ 5^{7} 	imes 5^{-4} 	imes 53 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$5^{7}	imes 5^{-4}	imes 53$$
- step1: Multiply the terms:
  $$5^{7-4}	imes 53$$
- step2: Subtract the numbers:
  $$5^{3}	imes 53$$
- step3: Evaluate the power:
  $$125	imes 53$$
- step4: Multiply:
  $$6625$$
Calculate or simplify the expression $$ \frac{y^{-2}}{3 y^{4}} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{y^{-2}}{3y^{4}}$$
- step1: Reduce the fraction:
  $$\frac{1}{3y^{4-\left(-2ight)}}$$
- step2: Reduce the fraction:
  $$\frac{1}{3y^{6}}$$
Calculate or simplify the expression $$ 6 x^{-3} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$6x^{-3}$$
- step1: Simplify:
  $$\frac{6}{x^{3}}$$
Calculate or simplify the expression $$ \left(3 a^{2}ight)^{-2} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(3a^{2}ight)^{-2}$$
- step1: Use the properties of exponents:
  $$3^{-2}\left(a^{2}ight)^{-2}$$
- step2: Evaluate the power:
  $$\frac{1}{9}a^{-4}$$
- step3: Simplify:
  $$\frac{1}{9a^{4}}$$
Calculate or simplify the expression $$ \frac{\left(3 a^{2}ight)^{3}}{a^{3}} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\left(3a^{2}ight)^{3}}{a^{3}}$$
- step1: Factor the expression:
  $$\frac{27a^{6}}{a^{3}}$$
- step2: Reduce the fraction:
  $$27a^{3}$$
Calculate or simplify the expression $$ \frac{\left(2^{3}ight)^{2}}{2^{4}} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(2^{3}ight)^{2}}{2^{4}}$$
- step1: Multiply the exponents:
  $$\frac{2^{3	imes 2}}{2^{4}}$$
- step2: Multiply by $$a^{-n}:$$
  $$2^{3	imes 2}	imes 2^{-4}$$
- step3: Multiply the numbers:
  $$2^{6}	imes 2^{-4}$$
- step4: Multiply:
  $$2^{6-4}$$
- step5: Subtract the numbers:
  $$2^{2}$$
- step6: Evaluate the power:
  $$4$$
Calculate or simplify the expression $$ (2 x)^{-4} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(2xight)^{-4}$$
- step1: Use the properties of exponents:
  $$2^{-4}x^{-4}$$
- step2: Evaluate the power:
  $$\frac{1}{16}x^{-4}$$
- step3: Simplify:
  $$\frac{1}{16x^{4}}$$
Calculate or simplify the expression $$ \left(4^{2}ight)^{-2} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(4^{2}ight)^{-2}$$
- step1: Multiply the exponents:
  $$4^{2\left(-2ight)}$$
- step2: Multiply the numbers:
  $$4^{-4}$$
- step3: Express with a positive exponent:
  $$\frac{1}{4^{4}}$$
- step4: Evaluate the power:
  $$\frac{1}{256}$$
Calculate or simplify the expression $$ 5^{2} 	imes 5^{3} 	imes 55 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$5^{2}	imes 5^{3}	imes 55$$
- step1: Multiply the terms:
  $$5^{2+3}	imes 55$$
- step2: Add the numbers:
  $$5^{5}	imes 55$$
- step3: Evaluate the power:
  $$3125	imes 55$$
- step4: Multiply:
  $$171875$$
Calculate or simplify the expression $$ \left(b^{3}ight)^{-4} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(b^{3}ight)^{-4}$$
- step1: Multiply the exponents:
  $$b^{3\left(-4ight)}$$
- step2: Multiply the numbers:
  $$b^{-12}$$
- step3: Simplify:
  $$\frac{1}{b^{12}}$$
Calculate or simplify the expression $$ \left(5^{-9} \cdot 5^{7}ight)^{-2} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(5^{-9}	imes 5^{7}ight)^{-2}$$
- step1: Multiply the numbers:
  $$\left(5^{-2}ight)^{-2}$$
- step2: Transform the expression:
  $$5^{-2\left(-2ight)}$$
- step3: Multiply the numbers:
  $$5^{4}$$
- step4: Evaluate the power:
  $$625$$
Calculate or simplify the expression $$ \left(2^{4}ight)^{2} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(2^{4}ight)^{2}$$
- step1: Multiply the exponents:
  $$2^{4	imes 2}$$
- step2: Multiply the numbers:
  $$2^{8}$$
- step3: Evaluate the power:
  $$256$$
Calculate or simplify the expression $$ 3^{3} 	imes 3^{2} 	imes 3^{5} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$3^{3}	imes 3^{2}	imes 3^{5}$$
- step1: Multiply the terms:
  $$3^{3+2+5}$$
- step2: Add the numbers:
  $$3^{10}$$
- step3: Evaluate the power:
  $$59049$$
Calculate or simplify the expression $$ \left(4 y^{3}ight)^{3} 	imes 6 y $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\left(4y^{3}ight)^{3}	imes 6y$$
- step1: Multiply the terms:
  $$384y^{9}	imes y$$
- step2: Multiply the terms:
  $$384y^{10}$$
Here are the simplified expressions for each of the problems:

1. $$ 5^{2} 	imes 5^{3} 	imes 55 = 171875 $$

2. $$ \left(b^{3}ight)^{-4} = \frac{1}{b^{12}} $$

3. $$ \left(4^{4}ight)^{5} \cup 20 $$ - This expression has a syntax error and cannot be simplified as is.

4. $$ \frac{4^{6}}{4^{4}} = 16 $$

5. $$ 3^{3} 	imes 3^{2} 	imes 3^{5} = 59049 $$

6. $$ \left(5^{-9} \cdot 5^{7}ight)^{-2} = 625 $$

7. $$ \left(2^{4}ight)^{2} = 256 $$

8. $$ \left(4 y^{3}ight)^{3} 	imes 6 y = 384y^{10} $$

9. $$ \left(\frac{3}{5}ight)^{2} = \frac{9}{25} $$

10. $$ 5^{7} 	imes 5^{-4} 	imes 53 = 6625 $$

11. $$ \frac{y^{-2}}{3 y^{4}} = \frac{1}{3y^{6}} $$

12. $$ 6 x^{-3} = \frac{6}{x^{3}} $$

13. $$ \frac{\left(3 a^{2}ight)^{3}}{a^{3}} = 27a^{3} $$

14. $$ x^{3} \cdot x^{-7} = \frac{1}{x^{4}} $$

15. $$ \left(3 a^{2}ight)^{-2} = \frac{1}{9a^{4}} $$

16. $$ (2 x)^{-4} = \frac{1}{16x^{4}} $$

17. $$ \left(4 d^{5}ight)^{-3} = \frac{1}{64d^{15}} $$

If you have any further questions or need additional assistance, feel free to ask!
Here are the simplified expressions for each problem: 1. $$ 5^{2} 	imes 5^{3} 	imes 55 = 171875 $$ 2. $$ \left(b^{3}ight)^{-4} = \frac{1}{b^{12}} $$ 3. $$ \left(4^{4}ight)^{5} 	imes 20 = 256 	imes 20 = 5120 $$ 4. $$ \frac{4^{6}}{4^{4}} = 16 $$ 5. $$ 3^{3} 	imes 3^{2} 	imes 3^{5} = 59049 $$ 6. $$ \left(5^{-9} \cdot 5^{7}ight)^{-2} = 625 $$ 7. $$ \left(2^{4}ight)^{2} = 256 $$ 8. $$ \left(4 y^{3}ight)^{3} 	imes 6 y = 384y^{10} $$ 9. $$ \left(\frac{3}{5}ight)^{2} = \frac{9}{25} $$ 10. $$ 5^{7} 	imes 5^{-4} 	imes 53 = 6625 $$ 11. $$ \frac{y^{-2}}{3 y^{4}} = \frac{1}{3y^{6}} $$ 12. $$ 6 x^{-3} = \frac{6}{x^{3}} $$ 13. $$ \frac{\left(3 a^{2}ight)^{3}}{a^{3}} = 27a^{3} $$ 14. $$ x^{3} \cdot x^{-7} = \frac{1}{x^{4}} $$ 15. $$ \left(3 a^{2}ight)^{-2} = \frac{1}{9a^{4}} $$ 16. $$ (2 x)^{-4} = \frac{1}{16x^{4}} $$ 17. $$ \left(4 d^{5}ight)^{-3} = \frac{1}{64d^{15}} $$ If you have any further questions or need additional assistance, feel free to ask!

CHAPTER 6 REVIEW
Simplify the following expressions. Reduce to simplest form. Make all exponents positive.

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