Solve (- 2m ^ 5 * n ^ 4) ^ 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

$$(-2m^{5}n^{4})^{3}$$

Evaluate

$-8n^{12}m^{15}$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-2m^{5}n^{4}\right)^{3}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(-2\right)^{3}\left(m^{5}\right)^{3}\left(n^{4}\right)^{3}$$

Raise $-2$ to the power $3$.

$$-8\left(m^{5}\right)^{3}\left(n^{4}\right)^{3}$$

To raise a power to another power, multiply the exponents.

$$-8m^{5\times 3}n^{4\times 3}$$

Multiply $5$ times $3$.

$$-8m^{15}n^{4\times 3}$$

Multiply $4$ times $3$.

$$-8m^{15}n^{12}$$

Expand

$-8n^{12}m^{15}$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-2m^{5}n^{4}\right)^{3}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(-2\right)^{3}\left(m^{5}\right)^{3}\left(n^{4}\right)^{3}$$

Raise $-2$ to the power $3$.

$$-8\left(m^{5}\right)^{3}\left(n^{4}\right)^{3}$$

To raise a power to another power, multiply the exponents.

$$-8m^{5\times 3}n^{4\times 3}$$

Multiply $5$ times $3$.

$$-8m^{15}n^{4\times 3}$$

Multiply $4$ times $3$.

$$-8m^{15}n^{12}$$