Skip to main content
Ch. P - Fundamental Concepts of Algebra
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. P - Fundamental Concepts of AlgebraProblema 93
Capitolo 1, Problema 93

Simplify using properties of exponents. 20x125x14\(\frac{20x^{\frac{1}{2}\)}}{5x^{\(\frac{1}{4}\)}}

Guida verificata passo dopo passo
1
Identify the expression to simplify: \(\frac{20x^{\frac{1}{2}}}{5x^{\frac{1}{4}}}\).
Simplify the coefficients (numerical parts) by dividing 20 by 5: \(\frac{20}{5} = 4\).
Apply the quotient rule for exponents to the variable part: \(\frac{x^{\frac{1}{2}}}{x^{\frac{1}{4}}} = x^{\frac{1}{2} - \frac{1}{4}}\).
Subtract the exponents: \(\frac{1}{2} - \frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{1}{4}\), so the variable part becomes \(x^{\frac{1}{4}}\).
Combine the simplified coefficient and variable parts to write the simplified expression: \(4x^{\frac{1}{4}}\).

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
1m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Properties of Exponents

Properties of exponents are rules that simplify expressions involving powers of the same base. Key properties include the quotient rule, which states that when dividing like bases, subtract the exponents (a^m / a^n = a^(m-n)). These rules help in simplifying expressions with fractional exponents.
Video consigliato:
04:06
Rational Exponents

Fractional Exponents

Fractional exponents represent roots and powers simultaneously. For example, x^(1/2) means the square root of x, and x^(1/4) means the fourth root of x. Understanding how to manipulate fractional exponents is essential for simplifying expressions involving roots.
Video consigliato:
04:06
Rational Exponents

Simplifying Rational Expressions

Simplifying rational expressions involves reducing fractions by factoring and canceling common terms. When variables with exponents appear in numerator and denominator, apply exponent rules to combine or reduce terms, making the expression simpler and easier to interpret.
Video consigliato:
05:07
Simplifying Algebraic Expressions
Pratica correlata
Domanda del libro di testo

Factor completely, or state that the polynomial is prime. 64-x^2

1042
views
Domanda del libro di testo

Simplify using properties of exponents.(x23)3(x^{\(\frac\)23})^3

769
views
Domanda del libro di testo

Perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (8.4×108)/(4×105)(8.4×10^8)/(4×10^5)

842
views
Domanda del libro di testo

In Exercises 93–102, factor and simplify each algebraic expression. x3/4−x1/4

108
views
Domanda del libro di testo

Perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (4.3×108)(6.2×104)(4.3×10^8)(6.2×10^4)

1009
views
Domanda del libro di testo

In Exercises 85–96, simplify each algebraic expression. 7−4[3−(4y−5)]

230
views