Exam 5: Exponents, Polynomials, and Polynomial Functions

Solve the problem. Express your answer in scientific notation, rounding as needed. -A computer can do one calculation in $1.4 \times 10^{-7}$ seconds. How long would it take the computer to do a trillion $\left(10^{12}\right)$ calculations?

Give the numerical coefficient and the degree of the term. -11

Decide whether the expression has been simplified correctly. - $x y^{0}=x$

Decide whether the expression has been simplified correctly. - $\left(\frac{\mathrm{a}}{4}\right)^{9}=\frac{\mathrm{a}^{9}}{4^{9}}$

Apply the quotient rule for exponents, if applicable, and write the result using only positive exponents. Assume all variables represent nonzero numbers. - $\frac{x^{-16}}{x^{-16}}$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. Also give the degree. - $-15 x$

Find the product - $(4.9 x-6 y)(3 x+2 y)$

Add or subtract as indicated. - $\left(-6 x^{3}+9 x^{2}+4\right)-\left(-5 x^{3}+2 x-5\right)$

Find the product - $\left(5 x-\frac{1}{2} y\right)(x+5 y)$

Find the product - $\left(\mathrm{q}-\frac{4}{7} \mathrm{r}\right)^{2}$

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers. - $\left(x^{-2} y^{6}\right)^{-4}$

Is it true that in order to multiply a number by a positive power of ten, you must move the decimal point to the left as many places as indicated by the exponent on the ten?

Find the product - $(x-3)(-5 x-9)$

Is it true that $6 \times 10^{-14}$ is written in scientific notation?

Find ( $f(g)(x)$ for the given functions $f(x)$ and $g(x)$ . - $f(x)=7 x+7$ and $g(x)=x^{2}-5$

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers. - $\left(6^{-1} \cdot 7^{-2}\right)^{-4}$

For the pair of functions, find the quotient $\left(\frac{f}{g}\right)(x)$ and give any $x$ -values that are not in the domain of the quotient function. - $f(x)=10 x^{2}+2 x, g(x)=2 x$

Tell whether the statement is . -A polynomial of degree 4 has 4 terms.

Combine terms. - $-12 y^{3}-4 y-3 y^{3}+5$

Graph the function. - $r(x)=x^{3}-2 x+2$