Solve 10t ( x^ -2 y^ -6 z x^ -5 y^ 10 z^ -3 )^ -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

$$( \frac { x ^ { - 2 } y ^ { - 6 } z } { x ^ { - 5 } y ^ { 10 } z ^ { - 3 } } ) ^ { - 2 }$$

Evaluate

$\frac{y^{32}}{x^{6}z^{8}}$

Solution Steps

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

$$\left(\frac{y^{-6}x^{3}z^{4}}{y^{10}}\right)^{-2}$$

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

$$\left(\frac{x^{3}z^{4}}{y^{16}}\right)^{-2}$$

To raise $\frac{x^{3}z^{4}}{y^{16}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{3}z^{4}\right)^{-2}}{\left(y^{16}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply $16$ and $-2$ to get $-32$.

$$\frac{\left(x^{3}z^{4}\right)^{-2}}{y^{-32}}$$

Expand $\left(x^{3}z^{4}\right)^{-2}$.

$$\frac{\left(x^{3}\right)^{-2}\left(z^{4}\right)^{-2}}{y^{-32}}$$

To raise a power to another power, multiply the exponents. Multiply $3$ and $-2$ to get $-6$.

$$\frac{x^{-6}\left(z^{4}\right)^{-2}}{y^{-32}}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $-2$ to get $-8$.

$$\frac{x^{-6}z^{-8}}{y^{-32}}$$

Expand

$\frac{y^{32}}{x^{6}z^{8}}$

Solution Steps

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

$$\left(\frac{y^{-6}x^{3}z^{4}}{y^{10}}\right)^{-2}$$

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

$$\left(\frac{x^{3}z^{4}}{y^{16}}\right)^{-2}$$

To raise $\frac{x^{3}z^{4}}{y^{16}}$ to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{3}z^{4}\right)^{-2}}{\left(y^{16}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply $16$ and $-2$ to get $-32$.

$$\frac{\left(x^{3}z^{4}\right)^{-2}}{y^{-32}}$$

Expand $\left(x^{3}z^{4}\right)^{-2}$.

$$\frac{\left(x^{3}\right)^{-2}\left(z^{4}\right)^{-2}}{y^{-32}}$$

To raise a power to another power, multiply the exponents. Multiply $3$ and $-2$ to get $-6$.

$$\frac{x^{-6}\left(z^{4}\right)^{-2}}{y^{-32}}$$

To raise a power to another power, multiply the exponents. Multiply $4$ and $-2$ to get $-8$.

$$\frac{x^{-6}z^{-8}}{y^{-32}}$$