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akposevictor

Answer:

[tex] 3^{-3} [/tex] ÷ [tex] 3^{4} [/tex]

Step-by-step explanation:

Evaluate [tex] 3^3 [/tex] ÷ [tex] 3^{-4} [/tex], then evaluate each given expression to find which of them will give us the same result.

[tex] 3^3 [/tex] ÷ [tex] 3^{-4} [/tex]

[tex] 27 [/tex] ÷ [tex] \frac{1}{3^4} [/tex] (recall: [tex] a^{-x} = \frac{1}{a^x} [/tex]

[tex] 27 [/tex] ÷ [tex] \frac{1}{81} [/tex]

[tex] 27 * \frac{81}{1} [/tex] (changing from division operation to multiplication by flipping the fraction to our right upside down)

[tex] 27 * 81 = 2,187 [/tex]

Let's compare the expressions in the given options to the value we got above:

Option 1: 3*3⁶

= 3*729 = 2,187 (this is equal)

Option 2: 3⁷ ÷ 3⁰

= 2,187 ÷ 1 (recall: x⁰ = 1, therefore, 3⁰ = 1)

= 2,187 (this is equal)

Option 3: 3³ * 3⁴

= 27*81 = 2,187 (this is equal)

Option 4: [tex] 3^{-3} [/tex] ÷ [tex] 3^{4} [/tex]

[tex] \frac{1}{3^3} [/tex] ÷ [tex] 81 [/tex]

[tex] \frac{1}{27} [/tex] ÷ [tex] 81 [/tex]

[tex] \frac{1}{27} * \frac{1}{81} [/tex] (changing from division to multiplication)

[tex] = \frac{1*1}{27*81} [/tex]

[tex] = \frac{1}{2,187} [/tex] (not equal)

[tex] 3^{-3} [/tex] ÷ [tex] 3^{4} [/tex] i not equal to [tex] 3^3 [/tex] ÷ [tex] 3^{-4} [/tex].

The expression that is not equal to the given expression is; 3⁻³ × 3⁴

Laws of Exponents

We are given the expression; 3³ ÷ 3⁻⁴

According to laws of exponents, x⁵ ÷ x² = x⁽⁵ ⁻ ²⁾

Thus; 3³ ÷ 3⁻⁴ = 3⁽³ ⁻ ⁽⁻⁴⁾⁾ = 3⁷

Let us look at each of the options;

  • A) 3 × 3⁶ = 3⁽¹ ⁺ ⁶⁾

Adding the exponents gives ⇒ 3⁷

  • B) 3⁷ ÷ 3⁰ = 3⁽⁷ ⁻ ⁰⁾

Subtracting the exponents gives ⇒ 3⁷

  • C)  3³ × 3⁴ = 3⁽³ ⁺ ⁴⁾

Adding the exponents gives ⇒ 3⁷

D) 3⁻³ × 3⁴ = 3⁽⁻³ ⁺ ⁴⁾

Subtracting the exponents gives⇒ 3

Looking at the options, the only one that is not equal to the given expression is; 3⁻³ × 3⁴

Read more about Laws of exponents at; https://brainly.com/question/11761858

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