exponents and scientific notation math homework help

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Simplify the expression using properties of exponents.

Z4Z2

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a. z8

b. z6

c. z2

d. z16

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Simplify the expression using properties of exponents. Write your answer with positive exponents only. Assume that variables are not 0.

fraction numerator 4 y to the power of 8 z to the power of minus 2 end exponent over denominator 1 y z to the power of minus 3 end exponent end fraction

a. 4y7z

b. 4y7z5

c. fraction numerator 4 y to the power of 7 over denominator z to the power of 5 end fraction

d. fraction numerator 4 y to the power of 7 over denominator z end fraction

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Simplify the expression using properties of exponents. Write your answer with positive exponents only. Assume that variables are not 0.

fraction numerator 12 r to the power of 9 s to the power of 0 over denominator left parenthesis 2 s right parenthesis to the power of 0 end fraction

a. fraction numerator 6 r to the power of 9 over denominator s end fraction

b. 6r9

c. 12r9

d. fraction numerator 12 r to the power of 9 over denominator s end fraction

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Simplify the expression using properties of exponents. Write your answer with positive exponents only. Assume that variables are not 0.

fraction numerator 3 m to the power of x plus 1 end exponent over denominator 2 m to the power of x minus 1 end exponent end fraction

a. 3 over 2 m to the power of 2 x end exponent

b. 3 over 2 m squared

c. 3 over 2 m to the power of 2 x plus 2 end exponent

d. 3 over 2

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Simplify the expression using properties of exponents. Write your answer with positive exponents only. Assume that variables are not 0.

fraction numerator left parenthesis 2 y to the power of n plus 4 end exponent right parenthesis squared over denominator y to the power of 2 n plus 1 end exponent end fraction

a. 4y7

b. 4 over y to the power of n minus 5 end exponent

c. 4 over y to the power of n minus 3 end exponent

d. 4 over y to the power of n minus 7 end exponent

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Write the following number in scientific notation.

4,328,000,000

a. 432.8 × 105

b. 432.8 × 10-5

c. 4.328 × 10-9

d. 4.328 × 109

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Write the following number in standard notation.

3.4 × 10-6

a, 0.0000034

b. 0.00000034

c. 3,400,000

d. 34,000,000

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Which of the following shows the correct first step when multiplying the numbers below using scientific notation and properties of exponents?

(4.2 × 108)(3.6 × 10-4)

a. (4.2 × 3.6)(108 + 10-4)

b. (4.2 + 3.6)(108 × 10-4)

c. (4.2 + 3.6)(108 + 10-4)

d. (4.2 × 3.6)(108 × 10-4)

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Divide the numbers below and write your answer in scientific notation.

fraction numerator 1.5 space x space 10 to the power of 15 over denominator 3 space x space 10 to the power of 8 end fraction

a. 4.5 x 1023

b. 0.5 x 107

c. 5.0 x 106

d. 5.0 x 108

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Multiply the numbers below and write your answer in scientific notation. (4.5 × 106)(2.5 × 105)

a. 11.25 × 1030

b. 11.25 × 1011

c. 1.125 × 1010

d. 1.125 × 1012

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