Math Core

This test covers all of the Exponents unit: properties of exponents, zero and negative exponents, radicals and rational exponents, exponential functions, exponential growth and decay, and geometric sequences.

Question 1

Write $x^5 \cdot x^8$ as a single power $x^n$ . What is $n$ ?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 2

Simplify $(3x^4)^2$ .

Question 3

Write $\dfrac{(a^3)^4}{a^6}$ as a single power $a^n$ . What is $n$ ?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 4

Evaluate $6^{-2}$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 5

Simplify $\dfrac{x^{-2} y^3}{x^3 y^{-1}}$ and write it with positive exponents.

Question 6

Evaluate $64^{2/3}$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 7

Write $\sqrt{50}$ in simplest form as $a\sqrt{2}$ . What is $a$ ?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 8

Let $f(x) = 5 \cdot 2^x$ . Find $f(3)$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 9

Which function shows exponential decay?

Question 10

Which table could represent an exponential function?

Question 11

You invest $1,500 at $5\%$ interest compounded annually. How much is the investment worth after $4$ years? Round to the nearest cent.

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 12

A $120$ -gram sample has a half-life of $10$ years. How many grams remain after $30$ years?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 13

A car's value is modeled by $V = 24000(0.93)^t$ , where $t$ is in years. By what percent does the value decrease each year?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 14

Find the $10$ th term of the geometric sequence $3, 6, 12, 24, \dots$

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 15

A geometric sequence has $a_1 = 81$ and $r = -\tfrac{1}{3}$ . Find $a_5$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.