Question

Find each product. Assume all variables represent positive real numbers. ﻿−4k(k7/3−6k1/3)-4k \left( $$k^{7/3}$$ - $$6k^{1/3}$$ \right)
−4k(k7/3−6k1/3)

Accepted Answer

Start by distributing the term outside the parentheses, which is $$-4k$$, to each term inside the parentheses: $$-4k 	imes k$$^{7/3}$$ and -4k$$ 	imes $$(-6k^{1/3}$$)$$. Recall the property of exponents when multiplying like bases: a^m$$ 	imes a^n = $$a^{m+n}. $$Use this to combine the powers of $$k in $$each product. For the first product, add the exponents of $$k$$: $$1 ($$from $$k) $$plus $$\frac{7}{3} ($$from $$k^{7/3}$$), so the exponent becomes $$1 + \frac{7}{3}. $$For the second product, multiply the constants $$-4$$ and $$-6 to $$get a positive product, then add the exponents of $$k$$: $$1 ($$from $$k) $$plus $$\frac{1}{3} ($$from $$k^{1/3}$$), so the exponent becomes $$1 + \frac{1}{3}. $$Write the final expression as the sum of the two terms with their simplified coefficients and exponents, using the results from the previous steps.

Find each product. Assume all variables represent positive real numbers. $-4k \(\left\)( k^{7/3} - 6k^{1/3} \(\right\))$

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Key Concepts

Properties of Exponents

Distributive Property

Fractional Exponents

Find each product. Assume all variables represent positive real numbers. −4k(k7/3−6k1/3)-4k \(\left\)( k^{7/3} - 6k^{1/3} \(\right\))−4k(k7/3−6k1/3)