6.7 Integer exponents and scientific notation  (Page 7/10)

Coin production In 1942, the U.S. Mint produced 154,500,000 nickels. Write 154,500,000 in scientific notation.

Distance The distance between Earth and one of the brightest stars in the night star is 33.7 light years. One light year is about 6,000,000,000,000 (6 trillion), miles.

1. ⓐ Write the number of miles in one light year in scientific notation.
2. ⓑ Use scientific notation to find the distance between Earth and the star in miles. Write the answer in scientific notation.

Debt At the end of fiscal year 2015 the gross United States federal government debt was estimated to be approximately $18,600,000,000,000 ($18.6 trillion), according to the Federal Budget. The population of the United States was approximately 300,000,000 people at the end of fiscal year 2015.

1. ⓐ Write the debt in scientific notation.
2. ⓑ Write the population in scientific notation.
3. ⓒ Find the amount of debt per person by using scientific notation to divide the debt by the population. Write the answer in scientific notation.

1. ⓐ Explain the meaning of the exponent in the expression $2^3$ .
2. ⓑ Explain the meaning of the exponent in the expression $2^{\mathrm{-3}}$ .

When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative?

ⓐ $11c^4-23c^2+1$
ⓑ $9p^3+6p^2-p-5$
ⓒ $\frac{3}{7}x+\frac{5}{14}$
ⓓ 10
ⓔ $2y-12$

ⓐ $a^2-b^2$
ⓑ $24d^3$
ⓒ $x^2+8x-10$
ⓓ $m^2{n}^2-2mn+6$
ⓔ $7y^3+y^2-2y-4$

1. ⓐ $3x^2+9x+10$
2. ⓑ $14a^{2}bc$
3. ⓒ $6y+1$
4. ⓓ $n^3-4n^2+2n-8$
5. ⓔ $\mathrm{-19}$

1. ⓐ $5p^3-8p^2+10p-4$
2. ⓑ $\mathrm{-20}{q}^4$
3. ⓒ $x^2+6x+12$
4. ⓓ $23r^2{s}^2-4rs+5$
5. ⓔ 100

${\text{5y}}^{\text{3}}+8y^3$

$\mathrm{-14}k+19k$

$12q-(\mathrm{-6}q)$

$\mathrm{-9}c-18c$

$\text{12x}-4y-9x$

$3m^2+7n^2-3m^2$

$6x^{2}y-4x+8x{y}^2$

$\text{13a}+b$

$(5x^2+12x+1)+(6x^2-8x+3)$

$(9p^2-5p+3)+(4p^2-4)$

$(10m^2-8m-1)-(5m^2+m-2)$

$(7y^2-8y)-(y-4)$

Subtract
$\left(3s^2+10\right)\text{from}\left(15s^2-2s+8\right)$

Find the sum of $\left(a^2+6a+9\right)\text{and}\left(5a^3-7\right)$

Evaluate $3y^2-y+1$ when:

1. ⓐ $y=5$
2. ⓑ $y=\mathrm{-1}$
3. ⓒ $y=0$

Evaluate $10-12x$ when:

1. ⓐ $x=3$
2. ⓑ $x=0$
3. ⓒ $x=\mathrm{-1}$

Randee drops a stone off the 200 foot high cliff into the ocean. The polynomial $\mathrm{-16}{t}^2+200$ gives the height of a stone $t$ seconds after it is dropped from the cliff. Find the height after $t=3$ seconds.

A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of p dollars each is given by the polynomial $\mathrm{-4}{p}^2+460p.$ Find the revenue received when $p=75$ dollars.