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A) Step 1: Apply the negative exponent rule ((a)/(b))^-n = ((b)/(a))ⁿ.

May 15, 2026Mathematics

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2 parts

\frac{3}{2}

x^2 + 2x + 1

3 steps

Step 1: Apply the negative exponent rule $\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n$ .

\left(\frac{8}{27}\right)^{-\frac{1}{3}} = \left(\frac{27}{8}\right)^{\frac{1}{3}}

Apply the fractional exponent rule $a^{\frac{1}{n}} = \sqrt[n]{a}$ .
$\left(\frac{27}{8}\right)^{\frac{1}{3}} = \sqrt[3]{\frac{27}{8}}$
Calculate the cube root of the numerator and the denominator.
$\sqrt[3]{\frac{27}{8}} = \frac{\sqrt[3]{27}}{\sqrt[3]{8}} = \frac{3}{2}$
The answer is $\boxed{\frac{3}{2}}$ .

Step 1: Expand the expression $(x+1)^2$ using the formula $(a+b)^2 = a^2 + 2ab + b^2$ .

Here, $a=x$ and $b=1$ .

(x+1)^2 = x^2 + 2(x)(1) + 1^2

Simplify the expanded expression.
$x^2 + 2x + 1$
The answer is $\boxed{x^2 + 2x + 1}$ .

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