Apply the Properties of Integer Exponents to generate equivalent expressions to ((4 ^ 3* 7 ^ - 2) ^ - 5)/(7 ^ 9 * 4 ^ - 13) with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents (1 point)
sorry - you messed it up again!
(4^(-15) * 7^10) / (7^9 * 4^-13)
= 4^(-15+13) * 7^(10-9)
= 4^-2 * 7^1
= 7/16
My apologies for the mistake. You are correct.
To apply the properties of integer exponents and generate equivalent expressions with only positive exponents:
1. Start with the given expression: ((4^3 * 7^-2)^-5) / (7^9 * 4^-13)
2. Apply the product-to-power rule to simplify the exponents inside the parentheses:
((4^(3 * -5)) * (7^(-2 * -5))) / (7^9 * 4^-13)
= (4^(-15)) * (7^10) / (7^9 * 4^-13)
3. Combine the exponents by applying the power-of-a-power rule:
= 4^(-15 + 13) * 7^(10 - 9)
= 4^-2 * 7^1
= 1 / (4^2) * 7
= 1 / 16 * 7
= 7 / 16
Therefore, the simplified expression is 7 / 16.
To apply the properties of integer exponents and generate equivalent expressions with only positive exponents:
1. Start by applying the power of a product rule:
((4^3 * 7^-2)^-5)/(7^9 * 4^-13)
= (4^(3*-5) * 7^(-2*-5))/ (7^9 * 4^-13)
= (4^(-15) * 7^10) / (7^9 * 4^-13)
2. Now, apply the power of a power rule:
= 4^(-15*-1) * 7^(10*-1) / 7^9 * 4^-13
= 4^15 * 7^-10 / 7^9 * 4^-13
3. Use the power of a quotient rule:
= 4^15 / 4^13 * 7^-10/ 7^9
= 4^(15-13) * 7^(-10-9)
= 4^2 * 7^-19
= 16 / 7^19
No remaining exponents are left, and the simplified answer is 16/7^19.