Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$Express the following fraction in simplest form, only using positive exponents. (3(n^(-4))^(4))/(-15n^(9)) Answer:$

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{3\left(n^{-4}\right)^{4}}{-15 n^{9}}$ $\newline$ 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\left(n^{-4}\right)^{4}}{-15 n^{9}}

\newline

Answer:

Write & Identify: Write down the given expression and identify the negative exponent. $\newline$ The given expression is $(3(n^{-4})^4)/(-15n^9)$ . We have a negative exponent in the term $n^{-4}$ .
Apply Power Rule: Apply the power of a power rule to the term $(n^{-4})^4$ . According to the power of a power rule, $(a^m)^n = a^{m*n}$ . So, $(n^{-4})^4 = n^{-4*4} = n^{-16}$ .
Rewrite with Simplified Exponent: Rewrite the expression with the simplified exponent. $\newline$ The expression now becomes $(3n^{-16})/(-15n^9)$ .
Simplify Coefficients: Simplify the coefficients (numbers in front of the variables). $\newline$ Divide $3$ by $-15$ to simplify the coefficients. $\frac{3}{-15}$ simplifies to $-\frac{1}{5}$ .
Apply Quotient Rule: Apply the quotient of powers rule to the variable part. $\newline$ According to the quotient of powers rule, $a^{m}/a^{n} = a^{(m-n)}$ . So, $n^{-16}/n^{9} = n^{(-16-9)} = n^{-25}$ .
Rewrite with Simplified Variable: Rewrite the expression with the simplified variable part. $\newline$ The expression now becomes $(-\frac{1}{5})n^{-25}$ .
Convert Negative Exponent: Convert the negative exponent to a positive exponent. $\newline$ To convert a negative exponent to a positive exponent, we take the reciprocal of the base. So, $n^{-25}$ becomes $1/n^{25}$ .
Combine Coefficient & Variable: Combine the coefficient and the variable part with the positive exponent. $\newline$ The final simplified expression is $(-\frac{1}{5})(\frac{1}{n^{25}})$ , which can be written as $-\frac{1}{5n^{25}}$ .