((16x^(8))^((1)/(2)))/(12 x)

Apply Power of Power Rule: Identify the given expression and apply the power of a power rule. The expression is ((16x^(8))^((1)/(2)))/(12 x). According to the power of a power rule, (a^b)^c = a^(b*c). ((16x^(8))^((1)/(2)))/(12 x) = (16^(1/2) * (x^8)^(1/2))/(12 x)Simplify Powers of 16 and x^8: Simplify the powers of 16 and x^8. 16^(1/2) is the square root of 16, which is 4. (x^8)^(1/2) is the square root of x^8, which is x^4. So, (16^(1/2) * (x^8)^(1/2))/(12 x) becomes (4x^4)/(12 x).Simplify Fraction by Dividing: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. The greatest common divisor of 4 and 12 is 4. Divide both the numerator and the denominator by 4: (4/4)x^4 / (12/4)x. This simplifies to x^4 / 3x.Divide x^4 by x: Simplify the expression by dividing x^4 by x. When dividing like terms with exponents, subtract the exponents: x^4 / x = x^(4-1) = x^3. So, x^4 / 3x simplifies to x^3 / 3.

Home

Math Problems

Precalculus

Evaluate rational exponents

Full solution

\frac{\left(16 x^{8}\right)^{\frac{1}{2}}}{12 x}

Apply Power of Power Rule: Identify the given expression and apply the power of a power rule. $\newline$ The expression is $\frac{(16x^{8})^{\frac{1}{2}}}{12 x}$ . According to the power of a power rule, $(a^b)^c = a^{b*c}$ . $\newline$ $\frac{(16x^{8})^{\frac{1}{2}}}{12 x} = \frac{16^{\frac{1}{2}} \times (x^8)^{\frac{1}{2}}}{12 x}$
Simplify Powers of $16$ and $x^8$ : Simplify the powers of $16$ and $x^8$ . $16^{(1/2)}$ is the square root of $16$ , which is $4$ . $(x^8)^{(1/2)}$ is the square root of $x^8$ , which is $x^4$ . So, $(16^{(1/2)} \times (x^8)^{(1/2)})/(12 x)$ becomes $(4x^4)/(12 x)$ .
Simplify Fraction by Dividing: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. $\newline$ The greatest common divisor of $4$ and $12$ is $4$ . $\newline$ Divide both the numerator and the denominator by $4$ : $(\frac{4}{4}x^4) / (\frac{12}{4}x)$ . $\newline$ This simplifies to $x^4 / 3x$ .
Divide $x^4$ by $x$ : Simplify the expression by dividing $x^4$ by $x$ . When dividing like terms with exponents, subtract the exponents: $x^4 / x = x^{4-1} = x^3$ . So, $x^4 / 3x$ simplifies to $x^3 / 3$ .