Math Core

This test covers evaluating powers, the exponent rules (including zero and negative exponents), square and cube roots, and scientific notation.

Question 1

Evaluate $4^3$ .

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

Question 2

What is the value of $-2^4$ ?

Question 3

Evaluate $3 + 2 \cdot 3^2 + (4 - 2)^3$ .

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

Question 4

Write $6^3 \cdot 6^7$ as a single power $6^n$ . What is $n$ ?

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

Question 5

Write $(x^5)^4$ as a single power $x^n$ . What is $n$ ?

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

Question 6

Evaluate $9^0 + 2^{-1}$ .

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

Question 7

Which expression is equal to $(3y^4)^2$ ?

Question 8

Write $\dfrac{m^6 \cdot m^9}{m^{10}}$ as a single power $m^n$ . What is $n$ ?

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

Question 9

Evaluate $\sqrt{169}$ .

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

Question 10

The value of $\sqrt{45}$ is between which two consecutive whole numbers?

Question 11

Find all solutions of $x^2 - 4 = 32$ .

Separate answers with commas, e.g. 2, -5

Question 12

Evaluate $\sqrt[3]{-27}$ .

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

Question 13

Write 52,000,000 in scientific notation as $5.2 \times 10^n$ . What is $n$ ?

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

Question 14

Write $3.8 \times 10^{-3}$ in standard form.

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

Question 15

Multiply $(5 \times 10^6)(4 \times 10^2)$ . Write the answer in scientific notation as $2 \times 10^n$ . What is $n$ ?

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