How do you write the product of the expression #5^4*5^-7# using a positive exponent?

2 Answers
Nov 20, 2016

Answer:

#1/5^3#

Explanation:

Using the #color(blue)"laws of exponents"#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(a^mxxa^n=a^(m+n)" and " a^-mhArr1/a^m)color(white)(2/2)|)))#

#rArr5^4xx5^-7=5^-3=1/5^3#

Nov 20, 2016

Answer:

#1/5^3#

Explanation:

Another approach is to get rid of the negative index first..

Recall: #x^-m = 1/x^(+m)" and "x^m/x^n = 1/x^(n-m) if n>m#

#5^4 xx 5^-7#

=#5^4 xx 1/5^7#

=#1/5^(7-4)#

=#1/5^3#