Solve sqrt 9*9 *1*10^ -31 *10x1*6*10^ -19; 1 * 6 * 10 ^ - 19 * 10 ^ - 4 | 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

$$\sqrt{9\times9}\cdot1\times10^{-31}\times10x1\cdot6\times10^{-19}}; 1\cdot6\times10^{-19}\times10^{-4}$$

Evaluate

$\frac{27x_{1}}{5000000000000000000000000000000000000000000000000}$

Solution Steps

To multiply powers of the same base, add their exponents. Add $1$ and $-31$ to get $-30$.

$$1\times 6\times 10^{-30}\sqrt{9\times 9}x_{1}\times 10^{-19}$$

To multiply powers of the same base, add their exponents. Add $-30$ and $-19$ to get $-49$.

$$1\times 6\times 10^{-49}\sqrt{9\times 9}x_{1}$$

Multiply $1$ and $6$ to get $6$.

$$6\times 10^{-49}\sqrt{9\times 9}x_{1}$$

Calculate $10$ to the power of $-49$ and get $\frac{1}{10000000000000000000000000000000000000000000000000}$.

$$6\times \frac{1}{10000000000000000000000000000000000000000000000000}\sqrt{9\times 9}x_{1}$$

Multiply $6$ and $\frac{1}{10000000000000000000000000000000000000000000000000}$ to get $\frac{3}{5000000000000000000000000000000000000000000000000}$.

$$\frac{3}{5000000000000000000000000000000000000000000000000}\sqrt{9\times 9}x_{1}$$

Multiply $9$ and $9$ to get $81$.

$$\frac{3}{5000000000000000000000000000000000000000000000000}\sqrt{81}x_{1}$$

Calculate the square root of $81$ and get $9$.

$$\frac{3}{5000000000000000000000000000000000000000000000000}\times 9x_{1}$$

Multiply $\frac{3}{5000000000000000000000000000000000000000000000000}$ and $9$ to get $\frac{27}{5000000000000000000000000000000000000000000000000}$.

$$\frac{27}{5000000000000000000000000000000000000000000000000}x_{1}$$

Differentiate w.r.t. x_1

$\frac{27}{5000000000000000000000000000000000000000000000000} = 5.4 \times 10^{-48}$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add $1$ and $-31$ to get $-30$.

$$\frac{\mathrm{d}}{\mathrm{d}x_{1}}(1\times 6\times 10^{-30}\sqrt{9\times 9}x_{1}\times 10^{-19})$$

To multiply powers of the same base, add their exponents. Add $-30$ and $-19$ to get $-49$.

$$\frac{\mathrm{d}}{\mathrm{d}x_{1}}(1\times 6\times 10^{-49}\sqrt{9\times 9}x_{1})$$

Multiply $1$ and $6$ to get $6$.

$$\frac{\mathrm{d}}{\mathrm{d}x_{1}}(6\times 10^{-49}\sqrt{9\times 9}x_{1})$$

Calculate $10$ to the power of $-49$ and get $\frac{1}{10000000000000000000000000000000000000000000000000}$.

$$\frac{\mathrm{d}}{\mathrm{d}x_{1}}(6\times \frac{1}{10000000000000000000000000000000000000000000000000}\sqrt{9\times 9}x_{1})$$

Multiply $6$ and $\frac{1}{10000000000000000000000000000000000000000000000000}$ to get $\frac{3}{5000000000000000000000000000000000000000000000000}$.

$$\frac{\mathrm{d}}{\mathrm{d}x_{1}}(\frac{3}{5000000000000000000000000000000000000000000000000}\sqrt{9\times 9}x_{1})$$

Multiply $9$ and $9$ to get $81$.

$$\frac{\mathrm{d}}{\mathrm{d}x_{1}}(\frac{3}{5000000000000000000000000000000000000000000000000}\sqrt{81}x_{1})$$

Calculate the square root of $81$ and get $9$.

$$\frac{\mathrm{d}}{\mathrm{d}x_{1}}(\frac{3}{5000000000000000000000000000000000000000000000000}\times 9x_{1})$$

Multiply $\frac{3}{5000000000000000000000000000000000000000000000000}$ and $9$ to get $\frac{27}{5000000000000000000000000000000000000000000000000}$.

$$\frac{\mathrm{d}}{\mathrm{d}x_{1}}(\frac{27}{5000000000000000000000000000000000000000000000000}x_{1})$$

The derivative of $ax^{n}$ is $nax^{n-1}$.

$$\frac{27}{5000000000000000000000000000000000000000000000000}x_{1}^{1-1}$$

Subtract $1$ from $1$.

$$\frac{27}{5000000000000000000000000000000000000000000000000}x_{1}^{0}$$

For any term $t$ except $0$, $t^{0}=1$.

$$\frac{27}{5000000000000000000000000000000000000000000000000}\times 1$$

For any term $t$, $t\times 1=t$ and $1t=t$.

$$\frac{27}{5000000000000000000000000000000000000000000000000}$$