Question

Which expression is equivalent to StartFraction b Superscript negative 2 Baseline Over a b Superscript negative 3 Baseline EndFraction? Assume a not-equals 0, b not-equals 0.

Answer 1

Answer:

d e2020

Step-by-step explanation:

Answer 2

Answer:

• $\frac{b^{-2}}{ab^{-3}}=\frac{b}{a}$

Step-by-step explanation:

Writing the description in algebraic translation

$\frac{b^{-2}}{ab^{-3}}$

so we have to find the expression which will be equal to $\frac{b^{-2}}{ab^{-3}}$.

Considering the expression

$\frac{b^{-2}}{ab^{-3}}$

$\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}$

$\frac{b^{-2}}{b^{-3}}=b^{-2-\left(-3\right)}$

so the expression becomes

$=\frac{b^{-2-\left(-3\right)}}{a}$            ∵ $\frac{b^{-2}}{b^{-3}}=b^{-2-\left(-3\right)}$

$\mathrm{Subtract\:the\:numbers:}\:-2-\left(-3\right)=1$

$=\frac{b}{a}$

Therefore,

                    $\frac{b^{-2}}{ab^{-3}}=\frac{b}{a}$