Solve (3 ^ 3 * a ^ - 5 * b ^ 3) ^ 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

$$(3^{3}a^{-5}b^{3})^{3}$$

Evaluate

$\frac{19683b^{9}}{a^{15}}$

Solution Steps

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

$$\left(27a^{-5}b^{3}\right)^{3}$$

Expand $\left(27a^{-5}b^{3}\right)^{3}$.

$$27^{3}\left(a^{-5}\right)^{3}\left(b^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply $-5$ and $3$ to get $-15$.

$$27^{3}a^{-15}\left(b^{3}\right)^{3}$$

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

$$27^{3}a^{-15}b^{9}$$

Calculate $27$ to the power of $3$ and get $19683$.

$$19683a^{-15}b^{9}$$

Expand

$\frac{19683b^{9}}{a^{15}}$

Solution Steps

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

$$\left(27a^{-5}b^{3}\right)^{3}$$

Expand $\left(27a^{-5}b^{3}\right)^{3}$.

$$27^{3}\left(a^{-5}\right)^{3}\left(b^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply $-5$ and $3$ to get $-15$.

$$27^{3}a^{-15}\left(b^{3}\right)^{3}$$

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

$$27^{3}a^{-15}b^{9}$$

Calculate $27$ to the power of $3$ and get $19683$.

$$19683a^{-15}b^{9}$$