Pre-Algebra Mock Exam - Laws of Exponents

• 4

Answer explanation

The key word here is NOT! Remember, if the bases are not the same you must do the math. Once you calculate, you get 4^-5/1^-5.

When you have a negative exponent in your denominator and you can't use the quotient law, remember you will use the reciprocal to solve. 4/1 becomes 1/4 and the exponents are now all positive.

Answer explanation

Simplify -5/20 = -1/4

-1y⁶/4x^-3z⁵

Remember, whenever you have a negative exponent in your denominator you use the reciprocal. (Becareful, the (-3) exponent is only on the (x), it's not on the four.

=-x³y⁶/4z⁵

• All of the above

Answer explanation

Make sure you follow order of operations! It doesn't matter in this particular problem, but it does on some. (PEMDAS) 12² = 144,

2² = 4

144/4 = 36

Now select all of the choices that equal to 36 once you simplify.

Answer explanation

Start by identifying ALL of your exponents. 3¹, a² in your numerator. All of these exponents are raised to the power of 3.

Thus, your new numerator is 3³ a⁶. 3*3*3 = 27a⁶

In the denominator, 1/2 of 54a is 27a.

27a⁶ /27a = 1a⁵ or a⁵

• none of the above

Answer explanation

Please STOP applying the rules when the bases are different. Here, you must simply calculate and solve.

9^{2 =} 81

3⁴ = 3*3*3*3 = 81

81/81 = 1

Now select all of the choices that equal to 1.

Answer explanation

PEMDAS (I'm going to start with the paranthesis.

Again, a reminder, focus on your exponent. In the numerator, your exponents are: (3¹ a²)³ * a¹b³

= 3³a⁶ * a¹b³

The denominator exponents are: a²b³ * 3¹b¹

Multipliy the terms in your numerator and you get:

27a⁷b³

Multiply the terms in your denominator and you get:

a²3b⁴

27a⁷b³ / a² 3b⁴ (Quotient Law)

**Reminder, the ^-1 exponent is only on the variable b, not on (3).

= 27a⁵3b^-1 = 27a⁵ /3b =

=9a⁵ /b

Write the five laws of exponents using ONLY variables.

Answer explanation

A^m * Aⁿ = A^m+n

A^m / Aⁿ = A^m-n

A^-m = 1/A^m

A⁰ = 1

(A^m)ⁿ = A^m*n

Answer explanation

A negative exponent in your denominator lets you know you should use the reciprocal of the law.

1/A⁵ = A⁵/1

Now select all of the choices that = A⁵

Using the numbers -8 to 8, write a number in each box that will make the largest value possible. You can use a number ONLY ONCE!!!

Answer explanation

Remember that a negative number raised to a power that is an even number is a positive answer. For example, -2² = 4

-2 * -2

Thus, the two digits are -8⁸

Answer explanation

ANY number (excluding zero) raised to the power of zero is equal to 1. Make sure you are answering the question. The problem ask you to solve for "w".