Solve K = 3a ^ 2 * b * (4a * b ^ 2) ^ 2 | 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

$$K=3a^{2}b\times(4ab^{2})^{2}$$

Solve for K

$K=48a^{4}b^{5}$

Solution Steps

Expand $\left(4ab^{2}\right)^{2}$.

$$K=3a^{2}b\times 4^{2}a^{2}\left(b^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply $2$ and $2$ to get $4$.

$$K=3a^{2}b\times 4^{2}a^{2}b^{4}$$

Calculate $4$ to the power of $2$ and get $16$.

$$K=3a^{2}b\times 16a^{2}b^{4}$$

Multiply $3$ and $16$ to get $48$.

$$K=48a^{2}ba^{2}b^{4}$$

To multiply powers of the same base, add their exponents. Add $2$ and $2$ to get $4$.

$$K=48a^{4}bb^{4}$$

To multiply powers of the same base, add their exponents. Add $1$ and $4$ to get $5$.

$$K=48a^{4}b^{5}$$

Solve for a

$\left\{\begin{matrix}a=\frac{3^{\frac{3}{4}}\sqrt[4]{\frac{K}{b^{5}}}}{6}\text{; }a=-\frac{3^{\frac{3}{4}}\sqrt[4]{\frac{K}{b^{5}}}}{6}\text{, }&\left(K\leq 0\text{ and }b<0\right)\text{ or }\left(K\geq 0\text{ and }b>0\right)\\a\in \mathrm{R}\text{, }&K=0\text{ and }b=0\end{matrix}\right.$