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Popular >

simplify (3/2)^x(2/3)^x

Solution

simplify

(\frac{3}{2})^{x} (\frac{2}{3})^{x}

Solution

1^{x}

Solution steps

(\frac{3}{2})^{x} (\frac{2}{3})^{x}

Apply exponent rule:

a^{n} b^{n} = (a \cdot b)^{n}

(\frac{3}{2})^{x} (\frac{2}{3})^{x} = (\frac{3}{2} \cdot \frac{2}{3})^{x}

= (\frac{3}{2} \cdot \frac{2}{3})^{x}

Cross cancel:

\frac{a}{b} \cdot \frac{b}{a} = 1

\frac{3}{2} \cdot \frac{2}{3} = 1

= 1^{x}

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Frequently Asked Questions (FAQ)

What is (3/2)^x(2/3)^x ?
The solution to (3/2)^x(2/3)^x is 1^x