quivalent expression. (x^(6)*x^(7))/(x^(-8))

Combine Exponents: Combine the exponents in the numerator using the product rule for exponents. The product rule states that when you multiply two powers with the same base, you add the exponents. So, x^(6)*x^(7) becomes x^(6+7). Calculation: 6 + 7 = 13Apply Quotient Rule: Apply the quotient rule for exponents to divide the powers of x. The quotient rule states that when you divide two powers with the same base, you subtract the exponents. So, (x^(13))/(x^(-8)) becomes x^(13 - (-8)). Calculation: 13 - (-8) = 13 + 8 = 21Write Final Expression: Write the final simplified expression. The expression x^(13 - (-8)) simplifies to x^(21).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Equivalent expression. $\newline$ $(x^{6} \cdot x^{7}) / (x^{-8})$

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Equivalent expression.

\newline

(x^{6} \cdot x^{7}) / (x^{-8})

Combine Exponents: Combine the exponents in the numerator using the product rule for exponents. $\newline$ The product rule states that when you multiply two powers with the same base, you add the exponents. $\newline$ So, $x^{6}\times x^{7}$ becomes $x^{6+7}$ . $\newline$ Calculation: $6 + 7 = 13$
Apply Quotient Rule: Apply the quotient rule for exponents to divide the powers of $x$ . The quotient rule states that when you divide two powers with the same base, you subtract the exponents. So, $(x^{13})/(x^{-8})$ becomes $x^{13 - (-8)}$ . Calculation: $13 - (-8) = 13 + 8 = 21$
Write Final Expression: Write the final simplified expression. $\newline$ The expression $x^{13 - (-8)}$ simplifies to $x^{21}$ .