((16)/(81))^((3)/(4))

Identify Base and Exponent: Identify the base and the exponent in ((16)/(81))^((3)/(4)). In ((16)/(81))^((3)/(4)), Base: 16/81 Exponent: 3/4Express as Terms to Power: Express both the numerator and the denominator as terms raised to the power of 4. 16 = 2*2*2*2 = 2^4 81 = 3*3*3*3 = 3^4Rewrite with Individual Bases: Rewrite the expression using the individual bases raised to the power of 4. ((16)/(81))^((3)/(4)) = ((2^4)/(3^4))^((3)/(4))Apply Exponent Separately: Apply the exponent to both the numerator and the denominator separately. = (2^4)^(3/4) / (3^4)^(3/4)Simplify Exponents: Simplify the exponents by multiplying them. = 2^(4*(3/4)) / 3^(4*(3/4)) = 2^3 / 3^3Calculate Exponent Values: Calculate the values of the exponents. 2^3 = 2*2*2 = 8 3^3 = 3*3*3 = 27Write Final Simplified Value: Write the final simplified value. = 8 / 27

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$\left(\frac{16}{81}\right)^{\frac{3}{4}}$

View step-by-step help

Home

Math Problems

Algebra 2

Evaluate rational exponents

Full solution

\left(\frac{16}{81}\right)^{\frac{3}{4}}

Identify Base and Exponent: Identify the base and the exponent in $\left(\frac{16}{81}\right)^{\left(\frac{3}{4}\right)}$ . $\newline$ In $\left(\frac{16}{81}\right)^{\left(\frac{3}{4}\right)}$ , $\newline$ Base: $\frac{16}{81}$ $\newline$ Exponent: $\frac{3}{4}$
Express as Terms to Power: Express both the numerator and the denominator as terms raised to the power of $4$ . $\newline$ $16 = 2 \times 2 \times 2 \times 2$ $\newline$ $= 2^4$ $\newline$ $81 = 3 \times 3 \times 3 \times 3$ $\newline$ $= 3^4$
Rewrite with Individual Bases: Rewrite the expression using the individual bases raised to the power of $4$ . $\newline$ $\left(\frac{16}{81}\right)^{\frac{3}{4}} = \left(\frac{2^4}{3^4}\right)^{\frac{3}{4}}$
Apply Exponent Separately: Apply the exponent to both the numerator and the denominator separately. $\newline$ $= (2^4)^{\frac{3}{4}} / (3^4)^{\frac{3}{4}}$
Simplify Exponents: Simplify the exponents by multiplying them. $\newline$ $= 2^{4*(3/4)} / 3^{4*(3/4)}$ $\newline$ $= 2^3 / 3^3$
Calculate Exponent Values: Calculate the values of the exponents. $\newline$ $2^3 = 2\times2\times2 = 8$ $\newline$ $3^3 = 3\times3\times3 = 27$
Write Final Simplified Value: Write the final simplified value. $\newline$ $= \frac{8}{27}$