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In the given question we have to simplify each expression:

$鈸�\frac{x^{15}}{x^{10}}鈸�\frac{6^{14}}{6^5}鈸�\frac{x^{18}}{x^{22}}鈸�\frac{{12}^{15}}{{12}^{30}}$

To simplify an expression with a quotient, we need to first compare the exponents in the numerator and denominator.

Using Quotient Property,$\frac{a^m}{a^n}=a^{m鈭�n}$when$m>n$

Since $15>10$, there are more factors of$x$ in the numerator.
Use Quotient Property,

$\frac{x^{15}}{x^{10}}=x^{15-10}$

Simplify.

$\frac{x^{15}}{x^{10}}=x^5$

To simplify an expression with a quotient, we need to first compare the exponents in the numerator and denominator.

Using Quotient Property,$\frac{a^m}{a^n}=a^{m鈭�n}$when$m>n$

Since $14>5$, there are more factors of$x$ in the numerator.
Use Quotient Property,

$\frac{6^{14}}{6^5}=6^{14-5}$

Simplify.

$\frac{6^{14}}{6^5}=6^9$

To simplify an expression with a quotient, we need to first compare the exponents in the numerator and denominator.

Using Quotient Property, $\frac{a^m}{a^n}=\frac{1}{a^{m鈭�n}}$when$m<n$

Since $18<22$, there are more factors of$x$ in the denominator.
Use Quotient Property,

$\frac{x^{18}}{x^{22}}=\frac{1}{x^{22-18}}$

Simplify.

$\frac{x^{18}}{x^{22}}=\frac{1}{x^4}$

To simplify an expression with a quotient, we need to first compare the exponents in the numerator and denominator.

Using Quotient Property,$\frac{a^m}{a^n}=\frac{1}{a^{m鈭�n}}$when$m<n$

Since $15<30$, there are more factors of$x$ in the denominator.
Use Quotient Property,

$\frac{{12}^{15}}{{12}^{30}}=\frac{1}{{12}^{30-15}}$

Simplify.

$\frac{{12}^{15}}{{12}^{30}}=\frac{1}{{12}^{15}}$