Question

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. ﻿6y3(4y−1)−3/7−8y2(4y−1)4/7+16y(4y−$$1)11/76y^3(4y$$ - $$1)^{-3/7}$$ - $$8y^2(4y$$ - $$1)^{4/7} + 16y(4y$$ - $$1)^{11/7}
6y3(4y$$−1)−3/7−8y2(4y−1)4/7+16y(4y−1)11/7

Accepted Answer

Identify the variable expressions and their powers in each term: the terms are $$6y^{3}(4y-1$$)^{-3/7}$$, -8y$$^{2}$$(4y-1)^{4/7}$$, and $$16y^{1}(4y-1$$)^{11/7}$$. Determine the least power of each variable expression across all terms: for y$, the powers are 3, 2, and 1, so the least power is y$$^{1}$$; for (4y-1$$)$$, the powers are $$-\frac{3}{7}$$, $$\frac{4}{7}$$, and $$\frac{11}{7}$$, so the least power is (4y-1$$)^{-\frac{3}$${7}}. $$Factor out the least powers $$y^{1}(4y-1$$)^{-\frac{3}$${7}}$$ from each term, rewriting each term as a product of this factor and the remaining powers. Express each term inside the parentheses after factoring out as follows: for the first term, divide by the factored out expression; for the second and third terms, subtract the exponents of the factored out powers from their original exponents. Write the final factored expression as $$y(4y-1)^{-\frac{3}$${7}}$$ multiplied by the sum of the simplified terms inside the parentheses.

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. $6y^3(4y - 1)^{-3/7} - 8y^2(4y - 1)^{4/7} + 16y(4y - 1)^{11/7}$

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Factoring Out the Least Power

Properties of Exponents

Handling Variable Expressions with Exponents

Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. 6y3(4y−1)−3/7−8y2(4y−1)4/7+16y(4y−1)11/76y^3(4y - 1)^{-3/7} - 8y^2(4y - 1)^{4/7} + 16y(4y - 1)^{11/7} 6y3(4y−1)−3/7−8y2(4y−1)4/7+16y(4y−1)11/7