Perform the operation and simplify the answer fully. (8)/(5x^(3))÷(6x)/(7) Answer:

Divide Fractions as Multiplication: Write the division of fractions as multiplication by the reciprocal. To divide by a fraction, you multiply by its reciprocal. The reciprocal of (6x)/(7) is (7)/(6x). So, (8)/(5x^(3)) ÷ (6x)/(7) becomes (8)/(5x^(3)) * (7)/(6x).Multiply Numerators and Denominators: Multiply the numerators and denominators separately. Now, multiply the numerators (8 * 7) and the denominators (5x^(3) * 6x) separately. (8)/(5x^(3)) * (7)/(6x) = (8 * 7) / (5x^(3) * 6x).Perform Multiplication: Perform the multiplication. Calculate the multiplication of the numerators and denominators. (8 * 7) = 56 and (5x^(3) * 6x) = 30x^(4). So, (8)/(5x^(3)) * (7)/(6x) = 56 / (30x^(4)).Simplify Fraction: Simplify the fraction. To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 2 in this case. 56 / 2 = 28 and 30x^(4) / 2 = 15x^(4). So, 56 / (30x^(4)) simplifies to 28 / (15x^(4)).Write Final Expression: Write the final simplified expression. The fully simplified expression is 28 / (15x^(4)).

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Perform the operation and simplify the answer fully.

(8)/(5x^(3))÷(6x)/(7)
Answer:

Perform the operation and simplify the answer fully. $\newline$ $\frac{8}{5 x^{3}} \div \frac{6 x}{7}$ $\newline$ Answer:

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Perform the operation and simplify the answer fully.

\newline

\frac{8}{5 x^{3}} \div \frac{6 x}{7}

\newline

Answer:

Divide Fractions as Multiplication: Write the division of fractions as multiplication by the reciprocal. $\newline$ To divide by a fraction, you multiply by its reciprocal. The reciprocal of $(\frac{6x}{7})$ is $(\frac{7}{6x})$ . $\newline$ So, $(\frac{8}{5x^{3}}) \div (\frac{6x}{7})$ becomes $(\frac{8}{5x^{3}}) \times (\frac{7}{6x})$ .
Multiply Numerators and Denominators: Multiply the numerators and denominators separately. $\newline$ Now, multiply the numerators $(8 \times 7)$ and the denominators $(5x^{3} \times 6x)$ separately. $\newline$ $\frac{8}{5x^{3}} \times \frac{7}{6x} = \frac{8 \times 7}{5x^{3} \times 6x}$ .
Perform Multiplication: Perform the multiplication. $\newline$ Calculate the multiplication of the numerators and denominators. $\newline$ $(8 \times 7) = 56$ and $(5x^{3} \times 6x) = 30x^{4}$ . $\newline$ So, $\frac{8}{5x^{3}} \times \frac{7}{6x} = \frac{56}{30x^{4}}$ .
Simplify Fraction: Simplify the fraction. $\newline$ To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is $2$ in this case. $\newline$ $56 / 2 = 28$ and $30x^{4} / 2 = 15x^{4}$ . $\newline$ So, $56 / (30x^{4})$ simplifies to $28 / (15x^{4})$ .
Write Final Expression: Write the final simplified expression. $\newline$ The fully simplified expression is $\frac{28}{15x^{4}}$ .