Perform the operation and simplify the answer fully. (8)/(7x^(2))÷(2)/(3x^(3)) Answer:

Identify Operation: Identify the operation to be performed. We are dividing one fraction by another.Reciprocal Multiplication: Recall that dividing by a fraction is the same as multiplying by its reciprocal. So, we rewrite the division as a multiplication by the reciprocal of the second fraction. (8)/(7x^(2)) ÷ (2)/(3x^(3)) = (8)/(7x^(2)) * (3x^(3))/(2)Multiply Numerators and Denominators: Multiply the numerators and the denominators separately. (8 * 3x^(3)) / (7x^(2) * 2)Perform Multiplication: Perform the multiplication in the numerator and the denominator. 24x^(3) / 14x^(2)Simplify Fraction: Simplify the fraction by canceling out common factors. x^(2) can be canceled from both the numerator and the denominator, and the coefficients 24 and 14 can be simplified by dividing both by 2. (24/14) * (x^(3)/x^(2)) = (12/7) * x^(3-2)Simplify Exponents: Simplify the exponents by subtracting the powers (since we are dividing like bases) and reduce the fraction. (12/7) * x^(1) = 12x/7

Home

Math Problems

Precalculus

Operations with rational exponents

Full solution

Q. Perform the operation and simplify the answer fully.

\newline

\frac{8}{7 x^{2}} \div \frac{2}{3 x^{3}}

\newline

Answer:

Identify Operation: Identify the operation to be performed. We are dividing one fraction by another.
Reciprocal Multiplication: Recall that dividing by a fraction is the same as multiplying by its reciprocal. So, we rewrite the division as a multiplication by the reciprocal of the second fraction. $\newline$ $(8)/(7x^{2}) \div (2)/(3x^{3}) = (8)/(7x^{2}) \times (3x^{3})/(2)$
Multiply Numerators and Denominators: Multiply the numerators and the denominators separately. $\newline$ $(8 \times 3x^{3}) / (7x^{2} \times 2)$
Perform Multiplication: Perform the multiplication in the numerator and the denominator. $\frac{24x^{3}}{14x^{2}}$
Simplify Fraction: Simplify the fraction by canceling out common factors. $x^{2}$ can be canceled from both the numerator and the denominator, and the coefficients $24$ and $14$ can be simplified by dividing both by $2$ . $\newline$ $\left(\frac{24}{14}\right) \times \left(\frac{x^{3}}{x^{2}}\right) = \left(\frac{12}{7}\right) \times x^{3-2}$
Simplify Exponents: Simplify the exponents by subtracting the powers (since we are dividing like bases) and reduce the fraction. $\newline$ $(\frac{12}{7}) \times x^{1} = \frac{12x}{7}$