To apply the properties of integer exponents, we can multiply exponents when raising a power to a power, divide exponents when dividing powers with the same base, and subtract exponents when dividing powers with the same base but different exponents.
First, let's simplify the expression (4^3 × 7^(-2))^(-5) / (7^9 × 4^(-13)).
Applying the power of a product: (4^3 × 7^(-2))^(-5) is equal to 4^(3*(-5)) × 7^((-2)*(-5)).
So now our expression becomes:
4^(-15) × 7^10 / (7^9 × 4^(-13)).
Applying the power of quotient: 4^(-15) / 4^(-13) is equal to 4^((-15)-(-13)).
Now our expression becomes:
4^((-15)-(-13)) × 7^10 / 7^9.
Simplifying:
4^((-15)-(-13)) simplifies to 4^(-15+13) which is 4^(-2).
7^10 / 7^9 simplifies to 7^(10-9) which is 7^1.
Now our expression becomes:
4^(-2) × 7^1.
Finally, evaluating this expression:
4^(-2) is equal to 1/4^2 which is 1/16.
7^1 is equal to 7.
Putting it all together, the simplified expression is:
(1/16) × 7 which simplifies to 7/16.
Apply the properties of integer exponents to generate an expression equivalent to (4^3×7^-2)^-5/7^9×4^-13 with only positive exponents then solve the expression
It will be a simplified fraction with no remaining exponents
3 answers
9.(-33)0+3/5(8-27 0)
Apply the Zero Power Rule to create an equivalent expression to:
8 answers