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# Simplifying exponential equations

32. Zero exponent. Simplify each expression.
5y^2z(y^-3z^-1)

38. Changing the sign of an exponent. Write each expression without negative exponents and simplify.
5^-2xy^-3
3x^-2

52. The quotient rule for exponents. Simplify each expression.
2r^-3t^-1
10r^5t^2∙t^-3

64. Use the rules of exponents to simplify each expression.
2x^2∙5y^-5

72. For each equation find the integer that can be used as the exponent to make the equation correct.
1 over 125 = 5?

84. Scientific notation. Write each number in standard notation.
48 x 10^-3

90. Write each number in scientific notation.
8,200,100

96. Evaluate each expression using scientific notation without a calculator.
(6000)(0.00004)
(30,000)(0.002)

16. Raising an exponential expression to a power.
Assume the variables represent nonzero real numbers and use positive exponents only in your answer.
(m^-3)^-1(m^2)^-4

26. Raising a product to a power. Simplify.
(2x^-1y^2)^-3

36. Raising a quotient to a power.
(2a^2b)^-3
3

44. Simplify.
(-2/3)^-2

54. Variable exponents. Simplify each expression. Assume that the variables represent integers.
(5^4^-3y)^3(5^y^-2)^2

64. Summary of rules. Use the rules of exponents to simplify each expression if possible.
(-2y^4)^3
X

72. Use the rules of exponents to simplify each expression.
(3x^-1y^3)^-2 over (3xy^-1)^3 (9x^-9y^5)
NOTE THE LAST SET OF PARENTHESES ARE NEXT TO THE FIRST AND SECOND SET OF PARENTHESES

80. Write each expression as 2 raised to a power. Assume that the variables represent integers.
6^n^-5∙3^5^-n

#### Solution Preview

Please see attached files for detailed solutions

32. 5 / y
38. x^3 / ...

#### Solution Summary

A few examples of simplifying exponents is given.

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