Questions: UNIT 3 - CHALLENGE 3.1: Exponents 3-Negative Exponents LEARNING OBJECTIVE: Simplify an expression with negative exponents. Simplify the expression to a form In which x is raised to a single integer power. (x^6)^3 x^-3 / x^-4 a.) x^13 b.) x^11 c.) x^16 d.) x^19

UNIT 3 - CHALLENGE 3.1: Exponents

3-Negative Exponents
LEARNING OBJECTIVE: Simplify an expression with negative exponents.

Simplify the expression to a form In which x is raised to a single integer power.

(x^6)^3 x^-3 / x^-4

a.) x^13
b.) x^11
c.) x^16
d.) x^19

Transcript text: UNIT 3 - CHALLENGE 3.1: Exponents 3-Negative Exponents LEARNING OBJECTIVE: Simplify an expression with negative exponents. Simplify the expression to a form In which x is raised to a single integer power. \[ \frac{\left(x^{6}\right)^{3} x^{-3}}{x^{-4}} \] a.) $x^{13}$ b.) $x^{11}$ c.) $x^{16}$ d.) $x^{19}$

Solution

Solution Steps

To simplify the expression with negative exponents, we will apply the properties of exponents. First, use the power of a power property to simplify $(x^6)^3$. Then, combine the exponents in the numerator by adding them. Finally, simplify the expression by subtracting the exponent in the denominator from the combined exponent in the numerator.

Step 1: Simplify the Power of a Power

We start with the expression

\[ \frac{(x^{6})^{3} \cdot x^{-3}}{x^{-4}}. \]

Using the power of a power property, we simplify $(x^{6})^{3}$ as follows:

\[ (x^{6})^{3} = x^{6 \cdot 3} = x^{18}. \]

Step 2: Combine Exponents in the Numerator

Next, we combine the exponents in the numerator:

\[ x^{18} \cdot x^{-3} = x^{18 + (-3)} = x^{15}. \]

Step 3: Simplify the Entire Expression

Now, we simplify the entire expression by subtracting the exponent in the denominator from the combined exponent in the numerator:

\[ \frac{x^{15}}{x^{-4}} = x^{15 - (-4)} = x^{15 + 4} = x^{19}. \]