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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # Use the rules of exponents to simplify the following.  Question banks Downloads My Bookmarks Reviews Important topics
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Founder  Joined: 18 Apr 2015
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Use the rules of exponents to simplify the following. [#permalink]
Expert's post
Use the rules of exponents to simplify the following.

(a) $$(n^5)(n^{-3})$$

(b) $$(s^7)(t^7)$$

(c) $$\frac{r^{12}}{r^4}$$

(d) $$(\frac{2a}{b})^5$$

(e) $$(w^5)^{-3}$$

(f) $$(5^0)(d^3)$$

(g) $$\frac{(x^{10})(y^{-1})}{(x^{-5})(y^5)}$$

(h) $$\frac{(\frac{3x}{y})^2}{(\frac{1}{y})^5}$$

[Reveal] Spoiler: OA
(a) $$n^2$$ (b) $$(st)^7$$ (c) $$r^8$$ (d) $$\frac{32a^5}{b^5}$$ (e) $$\frac{1}{w^{15}}$$ (f) $$d^3$$ (g) $$\frac{x^{15}}{y^6}$$ (h) $$9x^2y^3$$

Math Review
Question: 5
Page: 244
Difficulty: medium

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GRE Instructor Joined: 10 Apr 2015
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Followers: 163

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Re: Use the rules of exponents to simplify the following. [#permalink]
Expert's post
Carcass wrote:
Use the rules of exponents to simplify the following.

(a) $$(n^5)(n^{-3})$$

(b) $$(s^7)(t^7)$$

(c) $$\frac{r^{12}}{r^4}$$

(d) $$(\frac{2a}{b})^5$$

(e) $$(w^5)^{-3}$$

(f) $$(5^0)(d^3)$$

(g) $$\frac{(x^{10})(y^{-1})}{(x^{-5})(y^5)}$$

(h) $$\frac{(\frac{3x}{y})^2}{(\frac{1}{y})^5}$$

[Reveal] Spoiler: OA
(a) $$n^2$$ (b) $$(st)^7$$ (c) $$r^8$$ (d) $$\frac{32a^5}{b^5}$$ (e) $$\frac{1}{w^{15}}$$ (f) $$d^3$$ (g) $$\frac{x^{15}}{y^6}$$ (h) $$9x^2y^3$$

Math Review
Question: 5
Page: 244
Difficulty: medium

(a) $$(n^5)(n^{-3})=n^{5+(-3)}=n^2$$

(b) $$(s^7)(t^7)=(st)^7$$

(c) $$\frac{r^{12}}{r^4}=r^{12-4}=r^8$$

(d) $$(\frac{2a}{b})^5=\frac{(2a)^5}{b^5}=\frac{2^5a^5}{b^5}=\frac{32a^5}{b^5}$$

(e) $$(w^5)^{-3}=w^{5 * -3}=w^{-15}=\frac{1}{w^{15}}$$

(f) $$(5^0)(d^3)=(1)(d^3)=d^3$$

(g) $$\frac{(x^{10})(y^{-1})}{(x^{-5})(y^5)}=(\frac{x^{10}}{x^{-5}})(\frac{y^{-1}}{y^5})=x^{15}y^{-6}=\frac{x^{15}}{y^6}$$

(h) $$\frac{(\frac{3x}{y})^2}{(\frac{1}{y})^5}=\frac{\frac{9x^2}{y^2}}{(\frac{1^5}{y^5})}=(\frac{9x^2}{y^2})(\frac{y^5}{1^5})=\frac{9x^2y^5}{y^2}=9x^2y^3$$

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Brent Hanneson – Creator of greenlighttestprep.com  Re: Use the rules of exponents to simplify the following.   [#permalink] 24 May 2019, 12:46
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