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2 months ago

Which shows the following expression after the negative exponents have been eliminated?

Mathematics

2 answers:

AnnZ [12.3K]2 months ago

7 0

Response:

$a^2b^2$

Detailed explanation:

Considering the given algebraic expression:

$\dfrac{a^3b^{-2}}{ab^{-4}}, a\neq 0, b\neq 0$

The task is to remove the negative exponents and derive the new expression.

Applying the Negative Exponent Rule: $x^{-y}=\dfrac{1}{x^y}$

Utilizing the Division Law for Exponents: $\dfrac{t^x}{t^y}=t^{x-y}$

Consequently:

$\dfrac{a^3b^{-2}}{ab^{-4}} = a^{3-1}\cdot b^{-2-(-4)}\\$Simplifying\\a^{3-1}\cdot b^{-2-(-4)}=a^2b^{-2+4}\\=a^2b^2\\Therefore:\\\dfrac{a^3b^{-2}}{ab^{-4}}=a^2b^2$

babunello [11.8K]2 months ago

5 0

Response:

Detailed explanation:

I completed the quiz.

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It is inferred that the authors of the sonnets belong to a certain poet from the Elizabethan era.

Step-by-step breakdown:

The details provided in the question are as follows:

Population mean, μ = 8.9

Sample mean, $\bar{x}$ = 10.2

Sample size, n = 6

Alpha, α = 0.05

Population standard deviation, σ = 2.5

Initially, we formulate the null hypothesis and the alternative hypothesis

To conduct this test, we utilize the One-tailed z test.

a) Equation:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

By substituting in all relevant values, we determine:

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