Solve ((3x ^ 2 * y ^ 3)/(4x ^ - 4 * y ^ 0)) ^ 3 | Equatix - Math Solver

Fractions & Decimals

Ratios & Proportions

Basic Number Theory

Integers & Absolute Values

Factors & Multiples

Prime Factorization

Basic Equations & Inequalities

Coordinate Plane & Graphing

Linear Equations & Inequalities

Quadratic Equations

Polynomials & Factoring

Functions & Graphs

Systems of Equations

Trigonometric Functions

Trigonometric Identities & Equations

Right Triangle Trigonometry

Graphing Trigonometric Functions

Limits & Continuity

Derivatives & Applications

Integrals & Applications

Series & Sequences

Multivariable Calculus

Functions & Graphs

Polynomial & Rational Functions

Exponential & Logarithmic Functions

Sequences & Series

Descriptive Statistics

Normal Distribution

Hypothesis Testing

Regression Analysis

Linear Programming

Sets & Counting

Eigenvalues & Eigenvectors

Linear Transformations

Atomic Structure

Thermochemistry

Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(\frac{3x^{2}y^{3}}{4x^{-4}y^{0}})^{3}$$

Evaluate

$\frac{27y^{9}x^{18}}{64}$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(\frac{3y^{3}x^{6}}{4}\right)^{3}$$

To raise $\frac{3y^{3}x^{6}}{4}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3y^{3}x^{6}\right)^{3}}{4^{3}}$$

Expand $\left(3y^{3}x^{6}\right)^{3}$.

$$\frac{3^{3}\left(y^{3}\right)^{3}\left(x^{6}\right)^{3}}{4^{3}}$$

To raise a power to another power, multiply the exponents. Multiply $3$ and $3$ to get $9$.

$$\frac{3^{3}y^{9}\left(x^{6}\right)^{3}}{4^{3}}$$

To raise a power to another power, multiply the exponents. Multiply $6$ and $3$ to get $18$.

$$\frac{3^{3}y^{9}x^{18}}{4^{3}}$$

Calculate $3$ to the power of $3$ and get $27$.

$$\frac{27y^{9}x^{18}}{4^{3}}$$

Calculate $4$ to the power of $3$ and get $64$.

$$\frac{27y^{9}x^{18}}{64}$$

Expand

$\frac{27y^{9}x^{18}}{64}$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(\frac{3y^{3}x^{6}}{4}\right)^{3}$$

To raise $\frac{3y^{3}x^{6}}{4}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3y^{3}x^{6}\right)^{3}}{4^{3}}$$

Expand $\left(3y^{3}x^{6}\right)^{3}$.

$$\frac{3^{3}\left(y^{3}\right)^{3}\left(x^{6}\right)^{3}}{4^{3}}$$

To raise a power to another power, multiply the exponents. Multiply $3$ and $3$ to get $9$.

$$\frac{3^{3}y^{9}\left(x^{6}\right)^{3}}{4^{3}}$$

To raise a power to another power, multiply the exponents. Multiply $6$ and $3$ to get $18$.

$$\frac{3^{3}y^{9}x^{18}}{4^{3}}$$

Calculate $3$ to the power of $3$ and get $27$.

$$\frac{27y^{9}x^{18}}{4^{3}}$$

Calculate $4$ to the power of $3$ and get $64$.

$$\frac{27y^{9}x^{18}}{64}$$