Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$Express the following fraction in simplest form, only using positive exponents. (3x^(-9))/((-4x^(-5))^(2)) Answer:$

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{3 x^{-9}}{\left(-4 x^{-5}\right)^{2}}$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Express the following fraction in simplest form, only using positive exponents.

\newline

\frac{3 x^{-9}}{\left(-4 x^{-5}\right)^{2}}

\newline

Answer:

Write Expression: Write down the given expression and identify the negative exponents. $\newline$ The given expression is $(3x^{-9})/((-4x^{-5})^{2})$ . $\newline$ We need to simplify this expression and express it with only positive exponents.
Apply Negative Exponent Rule: Apply the negative exponent rule, which states that $a^{-n} = \frac{1}{a^n}$ , to rewrite the expression with positive exponents. $\newline$ For the numerator, we have $3x^{-9}$ which becomes $\frac{3}{x^9}$ . $\newline$ For the denominator, we have $(-4x^{-5})^2$ . First, we'll deal with the exponent of $-5$ , which gives us $\left(-\frac{4}{x^5}\right)^2$ .
Simplify Denominator: Simplify the denominator by squaring both the coefficient and the variable part. $\newline$ $(-4/(x^5))^2$ becomes $(-4)^2/(x^5)^2$ , which simplifies to $16/(x^{10})$ .
Combine Fractions: Combine the simplified numerator and denominator to form a single fraction. $\newline$ We now have $(\frac{3}{x^9})/(\frac{16}{x^{10}})$ .
Divide Fractions: Divide the fractions by multiplying the numerator by the reciprocal of the denominator. $\newline$ This becomes $(\frac{3}{x^9}) \times (\frac{x^{10}}{16})$ .
Simplify Expression: Simplify the expression by canceling out common factors and applying the laws of exponents. $\newline$ The $x^9$ in the numerator and $x^{10}$ in the denominator can be simplified to $x^{(10-9)}$ in the numerator, which is $x^1$ or simply $x$ . $\newline$ The expression now is $(3 \times x)/16$ .
Final Expression: Write the final simplified expression with only positive exponents. $\newline$ The final simplified expression is $(\frac{3x}{16})$ .