The product of (-5a^2)^3•a^5 is [tex](-125) \times a^{11}[/tex]
Solution:
Given that we need to find the product of (-5a^2)^3•a^5
Some of the laws of exponents used to solve this sum are:
1) [tex]a^{m} \times a^{n}=a^{m+n}[/tex]
2) [tex]\frac{a^{m}}{a^{n}}=a^{m-n}[/tex]
Now solve the given expression,
[tex]\begin{array}{l}{\left(-5 a^{2}\right)^{3} \times a^{5}=(-5)^{3}\left(a^{2}\right)^{3} \times a^{5}} \\\\ {=(-5 \times-5 \times-5) \times\left(a^{6}\right) \times\left(a^{5}\right)} \\\\ {=(-125) \times\left(a^{6+5}\right)} \\\\ {=(-125) \times a^{11}}\end{array}[/tex]
Hence the product is [tex](-125) \times a^{11}[/tex]
