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3 years ago

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which expression is not equal to the expression shown? 3 to the 3rd power divided by 3 to the negative 4th power. Need the answe

r fast.

1 answer:

Alecsey [184]3 years ago

8 0

Answer:

$3^{-3}$ ÷ $3^{4}$

Step-by-step explanation:

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

$3^3$ ÷ $3^{-4}$

$27$ ÷ $\frac{1}{3^4}$ (recall: $a^{-x} = \frac{1}{a^x}$

$27$ ÷ $\frac{1}{81}$

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

$27 * 81 = 2,187$

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: $3^{-3}$ ÷ $3^{4}$

$\frac{1}{3^3}$ ÷ $81$

$\frac{1}{27}$ ÷ $81$

$\frac{1}{27} * \frac{1}{81}$ (changing from division to multiplication)

$= \frac{1*1}{27*81}$

$= \frac{1}{2,187}$ (not equal)

$3^{-3}$ ÷ $3^{4}$ i not equal to $3^3$ ÷ $3^{-4}$ .

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Option C:

$\frac{3 a^{2} b^{11}}{2 }$ is equivalent to the given expression.

Solution:

Given expression:

$$\frac{-18 a^{-2} b^{5}}{-12 a^{-4} b^{-6}}$

To find which expression is equivalent to the given expression.

$$\frac{-18 a^{-2} b^{5}}{-12 a^{-4} b^{-6}}$

Using exponent rule: $\frac{1}{a^m}=a^{-m}, \ \ \frac{1}{a^{-m}}=a^{m}$

$$=\frac{-18 a^{-2} b^{5}a^{4} b^{6}}{-12 }$

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$$=\frac{-18 a^{(-2+4)} b^{(5+6)}}{-12 }$

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Hence Option C is the correct answer.

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