# Chapter 5 - Section 5.7 - Negative Exponents and Scientific Notation - Exercise Set - Page 409: 63

$x^{8}$

#### Work Step by Step

Using the laws of exponents, the given expression, $(x^3)^5\cdot x^{-7} ,$ simplifies to \begin{array}{l}\require{cancel} x^{3(5)}\cdot x^{-7} \\\\= x^{15}\cdot x^{-7} \\\\= x^{15+(-7)} \\\\= x^{15-7} \\\\= x^{8} .\end{array}

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